research proposal for an experiment to search for the

Research Proposal for an Experiment toSearch for the Decay µ → eee

A. Blondel, A. Bravar, M. PohlDépartement de physique nucléaire et corpusculaire,

Université de Genève, Genève

S. Bachmann, N. Berger, M. Kiehn, A. Schöning, D. Wiedner, B. WindelbandPhysikalisches Institut, Universität Heidelberg, Heidelberg

P. Eckert, H.-C. Schultz-Coulon, W. ShenKirchoff Institut für Physik, Universität Heidelberg, Heidelberg

P. Fischer, I. PerićZentralinstitut für Informatik, Universität Heidelberg, Mannheim

M. Hildebrandt, P.-R. Kettle, A. Papa, S. Ritt, A. StoykovPaul Scherrer Institut, Villigen

G. Dissertori, C. Grab, R. WallnyEidgenössiche Technische Hochschule Zürich, Zürich

R. Gredig, P. Robmann, U. StraumannUniversität Zürich, Zürich

December 10th, 2012

Contents

Executive Summary 4

I Introduction 5

1 Motivation 6

2 Theory 82.1 Comparison µ → eee versus µ → eγ 92.2 Discussion of Specific Models . . . 102.3 Theory Summary . . . . . . . . . . 12

3 Experimental Situation 143.1 SINDRUM Experiment . . . . . . 143.2 MEG Experiment . . . . . . . . . . 143.3 Muon Conversion Experiments . . 153.4 LFV in τ Decays . . . . . . . . . . 153.5 LFV at the Large Hadron Collider 16

4 The Decay µ → eee 184.1 Kinematics . . . . . . . . . . . . . 184.2 Detector Acceptance . . . . . . . . 184.3 Backgrounds . . . . . . . . . . . . 18

II The Mu3e Experiment 21

5 Requirements for Mu3e 225.1 Goals of the Experiment . . . . . . 225.2 Challenges for the Experiment . . 22

6 Experimental Concept 246.1 Momentum Measurement with Re-

curlers . . . . . . . . . . . . . . . . 256.2 Baseline Design . . . . . . . . . . . 256.3 Building up the Experiment . . . . 266.4 The Phase I Experiment . . . . . . 276.5 The Phase II Experiment . . . . . 29

7 Muon Beam 30

7.1 General Beam Requirements . . . . 30

7.2 Beam for phase I running . . . . . 30

7.3 High intensity muon beamline forphase II running . . . . . . . . . . 32

8 Magnet 37

9 Stopping Target 39

9.1 Baseline Aluminium Design . . . . 39

9.2 Vertex distribution . . . . . . . . . 40

9.3 Alternative Designs . . . . . . . . . 40

10 The Mu3e Pixel Detector 43

10.1 HV-Maps Sensor . . . . . . . . . . 43

10.2 Sensor specification . . . . . . . . . 44

10.3 Path towards the Full Sensor . . . 44

10.4 Characterization of the Prototypes 46

10.5 Mechanics . . . . . . . . . . . . . . 49

10.6 Cooling . . . . . . . . . . . . . . . 51

10.7 Alternative Technologies . . . . . . 51

11 The Mu3e Fibre Detector 55

11.1 The time of flight detector . . . . . 55

11.2 Readout of photon detectors . . . . 57

11.3 GEANT simulations . . . . . . . . 58

12 The Mu3e Tile Detector 59

12.1 Detector Design . . . . . . . . . . . 59

12.2 Simulation . . . . . . . . . . . . . . 60

12.3 Time Resolution Measurements . . 61

12.4 Detector Prototype . . . . . . . . . 62

2

13 Data Acquisition 6313.1 Overview . . . . . . . . . . . . . . 6313.2 Occupancy . . . . . . . . . . . . . 6313.3 Front-end . . . . . . . . . . . . . . 6313.4 Read-out links . . . . . . . . . . . 6813.5 Read-out cards . . . . . . . . . . . 6913.6 Event filter interface . . . . . . . . 6913.7 Data collection . . . . . . . . . . . 6913.8 Slow control . . . . . . . . . . . . . 69

14 Online Event Selection 7114.1 Selection Algorithms . . . . . . . . 7114.2 Hardware Implementation . . . . . 71

15 Simulation 7415.1 Detector geometry . . . . . . . . . 7415.2 Magnetic field . . . . . . . . . . . . 7615.3 Physics Processes . . . . . . . . . . 7615.4 Time structure . . . . . . . . . . . 78

16 Reconstruction 7916.1 Track Reconstruction in the Pixel

Tracker . . . . . . . . . . . . . . . 7916.2 Track Fitting and Linking . . . . . 7916.3 Vertex Fitting . . . . . . . . . . . . 82

17 Sensitivity Study 8417.1 Simulation and Reconstruction

Software . . . . . . . . . . . . . . . 8417.2 Signal Acceptance . . . . . . . . . 8517.3 Selection . . . . . . . . . . . . . . . 8517.4 Results . . . . . . . . . . . . . . . . 89

III The Mu3e Collaboration 91

18 The Institutes in Mu3e 9218.1 Responsibilities . . . . . . . . . . . 9218.2 Collaborators . . . . . . . . . . . . 92

19 Schedule 9419.1 Phase I Schedule . . . . . . . . . . 9419.2 Phase II Schedule . . . . . . . . . . 94

20 Cost Estimates 95

A Appendix 96A.1 Mu3e theses . . . . . . . . . . . . . 96A.2 Acknowledgements . . . . . . . . . 96

Bibliography 96

Executive Summary

We propose an experiment (Mu3e) to search forthe lepton flavour violating (LFV) decay µ+ →e+e−e+. We aim for an ultimate sensitivity of onein 1016 µ-decays, four orders of magnitude betterthan previous searches. This sensitivity is madepossible by exploiting modern silicon pixel detect-ors providing high spatial resolution and hodo-scopes using scintillating fibres and tiles providingprecise timing information at high particle rates.

Existing beamlines available at PSI providingrates of order 108 muons per second allow to testfor the decay µ+ → e+e−e+ in one of 1015 muondecays. In a first phase of the experiment, weplan to make use of this and establish the experi-mental technique whilst at the same time pushingthe sensitivity by three orders of magnitude.

The installation of a new muon beamline at thespallation neutron source is currently under dis-cussion at PSI. Such a High Intensity Muon Beam(HiMB) will provide intensities in excess of 109

muons per second, which in turn are required toreach the aimed sensitivity of B(µ+ → e+e−e+) ∼10−16.

The proposed experiment is highly complement-ary to other LFV searches for physics beyond thestandard model, i.e. direct searches performed atthe Large Hadron Collider (LHC) and indirectedsearches in the decay of taus and muons, suchas the decay µ+ → e+γ, which is the subjectof the MEG experiment currently in operationat PSI. The proposed experiment for the searchµ+ → e+e−e+ will test lepton flavour violatingmodels of physics beyond the Standard Modelwith unprecedented sensitivity.

This sensitivity is experimentally achieved by anovel experimental design exploiting silicon pixeldetectors based on High Voltage Monolithic Act-

ive Pixel Sensors (HV-MAPS). This technologyprovides high granularity, important for precisiontracking and vertexing, and allows one to signi-ficantly reduce the material budget by thinningdown the sensors and by integrating the hit digit-isation and readout circuitry in the sensor itself.The detector geometry is optimized to reach thehighest possible momentum resolution in a mul-tiple Coulomb scattering environment, which isneeded to suppress the dominating backgroundfrom the radiative muon decay with internal con-version, µ → eeeνν. The time information of thedecay electrons1, obtained from the pixel detectoris further improved by a time-of-flight system con-sisting of a scintillating fiber hodoscope and tileswith Silicon Photo-Multipliers (SiPM) for lightdetection. By combining both detector systemsaccidental background can be reduced below theaimed sensitivity of B(µ+ → e+e−e+) ∼ 10−16.

We will complete the sensor development andstart constructing the detector in 2013, in orderto be ready for first exploratory data taking at anexisting beam line with a first minimal detectorsetup in 2015. A detector capable of taking datarates of order 108 muons per second and capableof reaching a sensitivity of B(µ+ → e+e−e+) ∼10−15 will be available in 2016. This Phase I de-tector is the main focus of this proposal.

In Phase II, beyond 2017, the experiment willreach the ultimate sensitivity by exploiting a pos-sible new high intensity muon beamline with anintensity of > 2 · 109 muons per second. In theabsence of a signal, LFV muon decays can thenbe excluded for B(µ+ → e+e−e+)< 10−16 at 90 %confidence level.

1Here and in the following, the term “electron” denotesgenerically both decay electrons and positrons.

4

Part I

Introduction

5

Chapter 1

Motivation

In the Standard Model (SM) of elementaryparticle physics, the number of leptons of eachfamily (lepton flavour) is conserved at tree level.In the neutrino sector, lepton flavour violation(LFV) has however been observed in the formof neutrino mixing by the Super-Kamiokande [1],SNO [2], KamLAND [3] and subsequent experi-ments. Consequently, lepton flavour is a brokensymmetry, the standard model has to be adap-ted to incorporate massive neutrinos and leptonflavour violation is also expected in the chargedlepton sector. The exact mechanism and size ofLFV being unknown, its study is of large interest,as it is linked to neutrino mass generation, CPviolation and new physics beyond the SM (BSM).

The non-observation of LFV of charged leptonsin past and present experiments might at a firstglance be surprising, as the mixing angles in theneutrino matrix have been measured to be large(maximal). This huge suppression of LFV effectsis however accidental and due to the fact that (a)neutrinos are so much lighter than charged leptonsand (b) the mass differences between neutrinos(more precisely the square of the mass differences)are very small compared to the W-boson mass.

The situation completely changes if newparticles beyond the SM are introduced. If e.g.SUSY is realized at the electroweak scale, thescalar partners of the charged leptons (sleptons)will have large masses, and if not fully degener-ate, induce LFV interactions via loop corrections.These LFV effects from new particles at the TeVscale are naturally generated in many models andare therefore considered to be a prominent signa-ture for new physics.

In many extensions of the SM, such as grandunified models [4–6], supersymmetric models [7](see Figure 2.2), left-right symmetric models [8–10], models with an extended Higgs sector [11]and models where electroweak symmetry is brokendynamically [12], an experimentally accessibleamount of LFV is predicted in a large region ofthe parameter space.

Seesaw and Left-Right symmetric (supersym-metric) models are good candidates for realisinggrand unification, which also unify quark andlepton mass matrices. Moreover, it has beenshown that LFV effects in the low energy limitcan be related to mixing parameters at the GUTscale or to heavy Majorana masses in these mod-els [17, 18]. Seesaw models are therefore very at-tractive in the context of LFV as they are also ableto naturally explain the smallness of the masses ofthe left handed neutrinos. In this context the re-cent results from neutrino oscillation experimentsare very interesting, as they measured a large mix-ing angle θ13, which enhances the LFV-muon de-cays in most models which try to explain the smallneutrino masses and the large mixing.

Currently the most accurate measurement isprovided by the Daya Bay reactor neutrino ex-periment [19] yielding sin2(2θ13) = 0.089 ±0.010(stat) ± 0.005(syst), excluding the no-oscillation hypothesis at 7.7 standard deviantions.The Daya Bay measurement is in good agreementwith measurements by the RENO [20], DoubleChooz [21] and T2K [22] experiments. Theseresults are very encouraging, as large values ofsin2 (2θ13) lead to large LFV effects in many BSMmodels.

6

An Experiment to Search for the Decay µ → eee

Decay channel Experiment Branching ratio limit Reference

µ → eγ MEGA < 1.2 · 10−11 [13]MEG < 2.4 · 10−12 [14]

µ → eee SINDRUM < 1.0 · 10−12 [15]µ Au → eAu SINDRUM II < 7 · 10−13 [16]

Table 1.1: Experimental limits on LFV muon decays

The observation of LFV in the charged leptonsector would be a sign for new physics, possiblyat scales far beyond the reach of direct observa-tion at the large hadron collider (LHC). Severalexperiments have been performed or are in opera-tion to search for LFV in the decays of muons ortaus. Most prominent are the search for the radi-ative muon decay µ → eγ [13,14,23,24], the decayµ → eee [15], the conversion of captured muons toelectrons [16] and LFV tau decays [25–43].

The recent search performed by the MEG-Collaboration yields B(µ → eγ)< 2.4 · 10−12 [14]and sets currently the most stringent limit onmany LFV models. The MEG collaboration plansto continue operation into 2013 in order to in-crease the number of stopped muons and to reacha sensitivity of a few times 10−13. Plans to up-

grade the experiment to further improve the sens-itivity are currently under discussion.

In the near future the DeeMe experiment[44] at J-PARC plans to improve the currentmuon-to-electron conversion limit of B(µ Au →e Au)< 7 · 10−13 [16] by almost two orders of mag-nitude. By the end of the decade this limit couldbe improved by even four orders of magnitudeby COMET at J-PARC [45] and Mu2e at Fer-milab [46,47].

Selected limits for lepton flavour violating muondecays and muon-to-electron conversion experi-ments, which are of high relevance for the pro-posed experiment, are shown in Table 1.1. Asearch for the LFV decay µ → eee with an unpre-cedented sensitivity of < 10−16 as proposed herewould provide a unique opportunity for discover-ies of physics beyond the SM in the coming years.

7

Chapter 2

Theory

In the SM, charged lepton flavour violating reac-tions are forbidden at tree level and can only be in-duced by lepton mixing through higher order loopdiagrams. However, the dominant neutrino mix-ing loop diagram, see Figure 2.1, is strongly sup-pressed in the SM with B ≪ 10−50 and thus giv-ing potentially high sensitivity to LFV reactionsin models beyond the Standard Model (BSM).

Such an example is shown in Figure 2.2, wherea γ/Z-penguin diagram is shown with new su-persymmetric (SUSY) particles running in a loop.These loop contributions are important basicallyfor all models, where new particle couplings toelectrons and muons are introduced. Lepton flavorviolation can also be mediated by tree couplingsas shown in Figure 2.3. These couplings couldbe mediated by new particles, like Higgs particlesor doubly charged Higgs particles, R-parity viol-ating scalar neutrinos or new heavy vector bo-sons, the latter being motivated by models withextra dimensions [48, 49]. These models usually

µ+ e+

+W

νµ νe

γ

e-

e+

*

Figure 2.1: Feynman diagram for the µ → eee pro-cess via neutrino mixing (indicated by the cross).

µ+ e+

χ0~

e~µ~

γ /Z

e-

e+

*

Figure 2.2: Diagram for lepton flavour violationinvolving supersymmetric particles.

also predict semihadronic decays of tau leptons orthe muon conversion process µq → eq′, which isexperimentally best tested in muon capture exper-iments.

µ

e

e

e

X

Figure 2.3: Diagram for lepton flavour violationat tree level.

8


The lepton flavor violating three electron decayof the muon can be mediated, depending on themodel, via virtual loop (Figure 2.2) and box dia-grams or via tree diagrams (Figure 2.3). The mostgeneral Lagrangian for this decay can be paramet-erized as [50] 1:

Lµ→eee =4GF

2[mµAR µRσµνeLFµν

+ mµAL µLσµνeRFµν

+ g1 (µReL) (eReL)

+ g2 (µLeR) (eLeR)

+ g3 (µRγµeR) (eRγµeR)

+ g4 (µLγµeL) (eLγµeL)

+ g5 (µRγµeR) (eLγµeL)

+ g6 (µLγµeL) (eRγµeR) + H.c. ]

(2.1)

The form factors AR,L describe tensor type (di-pole) couplings, mostly acquiring contributionsfrom the photon penguin diagram, whereas thescalar-type (g1,2) and vector-type (g3 − g6) formfactors can be regarded as four fermion contactinteractions, to which the tree diagram contrib-utes in leading order. In addition also off shellform factors from the penguin diagrams, whichare not testable in the µ → eγ decay contributeto g1 −g6 [51]. In case of non-zero dipole and four-fermion couplings also interference effects have tobe considered, which can be exploited to investig-ate violation of time reversal (T -invariance).

By neglecting higher order terms in me, thetotal branching ratio of the decay can be expressedby:

B(µ → eee) =g2

1 + g22

8+ 2 (g2

3 + g24) + g2

5 + g26

+ 32 eA2 (lnm2

µ

m2e

− 11/4)

+16 η eA√

g23 + g2

4

+8 η′ eA√

g25 + g2

5 ,

(2.2)

where the definition A2 = A2L + A2

R is used. Theterm proportional to A2 is logarithmically en-hanced and can be assigned to the photon penguin

1A representation of Lagrangian containing explicitlythe contributions from the loop and box diagrams can befound in [51].

diagram. The constants η and η′ are T -violatingmixing parameters. In case of a signal, the dif-ferent terms can be measured from the angulardistribution of µ → eee decay particles using apolarized muon beam.

2.1 Comparison µ → eee versus

µ → eγ

In the decay µ → eγ physics beyond the SM isonly tested by photon penguin diagrams, in con-trast to µ → eee where also tree, Z-penguin andbox diagrams contribute. To compare the newphysics mass scale reach between the processesµ → eee and µ → eγ a simplified model is chosen;it is assumed that the photon penguin diagramFigure 2.2 and the tree diagram Figure 2.3 arethe only relevant contributions. The Lagrangianthen simplifies to2:

LLF V =

[

mµ

(κ + 1)Λ2µRσµνeLFµν

]

γ−penguin

+

[

κ

(κ + 1)Λ2(µLγµeL) (eLγµeL)

]

tree

(2.3)

where for the contact interaction (“tree”) term ex-emplarily a left-left vector coupling is chosen. Inthis definition a common mass scale Λ is intro-duced and the parameter κ describes the ratio ofthe amplitudes of the vector-type (tree) term overthe tensor (γ − penguin) term.

Limits on the common mass scale Λ as ob-tained from the experimental bounds on B(µ →eγ)< 2.4 · 10−12 (90 % CL MEG 2011) and B(µ →eee)< 1.0 · 10−12 (90 % CL SINDRUM ) are shownin Figure 2.4 as function of the parameter κ. Ex-perimentally, for small values of κ (dipole coup-ling) the mass scale Λ is best constrained by theMEG experiment whereas the four fermion con-tact interaction region with κ & 10 is best con-strained by the SINDRUM experiment.

For comparison also a hypothetical ten timesimproved limit is shown for the MEG experiment(post-upgrade) and compared to the sensitivitiesof the proposed µ → eee experiment of 10−15

(phase I) and 10−16 (phase II). It can be seenthat in this simple model comparison high massscales Λ will be best constrained by the proposed

2A similar study was presented in [52]

9


Figure 2.4: Experimental limits and projected lim-its on the LFV mass scale Λ as a function of theparameter κ (see equation 2.3) assuming negligiblecontributions from Z0 penguins; based on [52].

µ → eee experiment for all values of κ already inphase I.

In case of dominating tensor couplings (A 6=0, κ → 0) a quasi model independent relationbetween the µ → eee decay rate and the µ → eγdecay rate can be derived:

B(µ → eee)

B(µ → eγ)≈ 0.006 (2.4)

This ratio applies for many supersymmetric mod-els, where LFV effects are predominantly medi-ated by gauge bosons and where the masses ofthe scalar leptons or gauginos are of electroweakscale. In these models, which are already heavilyconstrained or even excluded by the recent LHCresults, the sensitivity of the proposed Mu3e ex-periment in terms of branching ratio has to be twoorders of magnitude higher than that of the MEGexperiment in order to be competitive.

2.1.1 Z-penguin Contribution

However, besides the tree and γ-penguin dia-grams also the Z-penguin diagram can signific-antly contribute to the process µ → eee. TheZ-penguin diagram is of particular importance ifthe new physics scale is higher than the electro-magnetic scale, as can be easily derived from adimensional analysis. The enhancement of theZ-penguin contribution over the γ-penguin con-tribution and its non-decoupling behaviour when

Figure 2.5: Experimental limits and projected lim-its on the LFV mass scale Λ as a function of theparameter κ (see equation 2.3) assuming contri-butions from Z0 penguins ten times larger thanthe photon contribution.

going to high mass scales was discussed for LittleHiggs models [53, 54] as well as for several SUSYmodels [55–59]. SUSY models with R-parity viol-ation and right handed neutrinos received recentlyquite some attention in this context, as approxim-ate cancellations of different Z-diagram contribu-tions are not present in extended Minimum Super-Symmetric Standard Models (MSSM).

The effect of such an enhanced Z-penguin coup-ling, where the LFV contribution to the µ → eeeprocess is exemplarily enhanced by a factor often relative to the photon-penguin contribution,is shown in Figure 2.5. It can be seen that thesensitivity of the µ → eee process to new physicsis significantly enhanced at small values of κ andthat in such a case a sensitivity of 10−14 is alreadysufficient to be competitive with the µ → eγ pro-cess with a sensitivity of a few times 10−13.

2.2 Discussion of Specific Models

In the following, selected models are discussed inmore detail in the context of the proposed exper-iment.

2.2.1 Inverse Seesaw SUSY Model

Despite the fact that the most simple supersym-metric models with light squarks and gluinos were

10


0 500 1000 1500 2000 2500 3000

10 -21

10 -2010 -19

10 -18

10 -17

10 -16

10 -15

10 -14

10 -13

m 0 = M1 2 @GeVD

Ri

Figure 2.6: Inverse Seesaw SUSY Model: Contri-butions to B(µ → eee) as a function of m0 = M1/2

for a degenerate singlet spectrum with MR =10 TeV and M = 1011 GeV. The rest of thecMSSM parameters are set to A0 = −300 GeV,B0 = 0, tan β = 10 and sign(µ) = +. Solid linesrepresent individual contributions, γ (black), Z(blue) and h (red) whereas the dashed lines rep-resent interference terms, γ − Z (green), γ − h(purple) and Z − h (orange). Note that in thiscase h includes both Higgs and box contributions.Taken from [58].

recently excluded by LHC experiments [60–84]supersymmetry can still exist in nature, just athigher mass scales or in more complex realisations.In many of these realisations with a non-minimalparticle content the Z-penguin contribution dis-cussed above gets significantly enhanced.

As a first example results obtained by a super-symmetric model with an inverse seesaw mechan-ism [58] are discussed here. The inverse seesawmodel [85] constitutes a very appealing alternat-ive to the standard seesaw realization and can beembedded in a minimal extension of the MSSMby the addition of two extra gauge singlet su-perfields, with opposite lepton numbers. Similarto other models, e.g. flavour violating Higgs de-cays in the MSSM, the Z-penguin exhibits herea non-decoupling behaviour, which is shown inFigure 2.6 for an effective right-handed neut-rino mass of M = 1011 GeV and degeneratesterile neutrino masses of MR = 10 TeV. Atsmall mass scales m0 = M1/2 of the constrainedMSSM (cMSSM) the photon-mediated penguincontribution clearly dominates over the other con-tributions from Higgs-mediated penguin and Z-mediated penguin diagrams. This picture com-pletely changes at higher mass scales above 200-

10−13

10−12

10−11

10−10

10−9

0 500 1000 1500 2000 2500 3000 3500 4000

BR

(µ→

x)

mνR

eγ

3e

Figure 2.7: Supersymmetric SU(3)c × SU(2)L ×U(1)B−L × U(1)R Model: Branching ratios oflepton flavour violating processes as a functionof mνR for m0 = 800 GeV, M1/2 = 1200 GeV,tan β = 10, A0 = 0, vR =10 TeV, tan βR = 1.05,µR = −500 GeV, mAR

= 1000 GeV. The dashedred line is the predicted branching ratio for µ →eγ and the dashed blue line for µ → eee. Takenfrom [59].

300 GeV, where the Z-mediated penguin diagrambecomes dominant. The non-decoupling beha-viour of the Z-penguin is clearly visible which willallow to test this model at any SUSY mass scalefor the seesaw parameters given in this exampleat phase II of the proposed experiment.

2.2.2 Supersymmetric SU(3)c × SU(2)L ×U(1)B−L × U(1)R Model

This model represents a supersymmetric versionof the SM, minimally extended by additionalU(1)B−L × U(1)R symmetry groups [86,87]. Thismodel includes the generation of light neutrinomasses by the seesaw mechanism, can explain theobserved large neutrino mixing angles and canbe easily embedded into a SO(10) grand unifiedtheory. This model predicts an additional lightHiggs particle, which is expected to mix with thelightest MSSM Higgs particle, and has been re-cently studied also in the context of LFV pro-cesses [59]. Also in this study it is found that athigh SUSY mass scales the photon-mediated LFVpenguin diagrams are more suppressed than theZ-mediated LFV penguin diagrams and that thissuppression scales with m4

Z/m4SUSY as naively

expected from a dimensional analysis. Branch-ing ratio predictions for the processes µ → eeeand µ → eγ are shown in Figure 2.7 as func-tion of the right-handed neutrino mass mνR

for

11


the SUSY model parameters as given in the figurecaption. Also here it can be seen that for highmasses mνR

> 300 GeV the Z-mediated penguindiagram starts to contribute dominantly to theµ → eee process and that for mνR

> 1000 GeVthe µ → eee process is expected to have an evenhigher branching fraction than µ → eγ. For evenhigher masses the non-decoupling behaviour is vis-ible in the µ → eee prediction.

2.2.3 Other Models

The above discussed enhancement of the Z-mediated penguin diagram appears also in LittleHiggs Models with T-parity (LHT) where ratiosB(µ → eee)/B(µ → eγ) ≈ 0.02 − 1 have been pre-dicted [53, 54, 88, 89], or in Left-Right Symmetricmodels with additional Higgs triplets. LFV inter-actions in Higgs-triplet models can be also gener-ated directly in tree diagrams, see Figure 2.3.

In [11], these LFV violating effects are studiedin a model where the Higgs triplet is responsiblefor neutrino mass generation. Figure 2.8 showsthe predicted branching ratios for each of the threeLFV muon processes and for different realisationsof the neutrino mass hierarchy. Note that the ab-solute value of the branching ratios depends onthe mass scale M and can vary. For the hier-archical case, Figure 2.8 b), all branching ratiosare expected to be of similar size whereas for thedegenerate, Figure 2.8 a), and the inverted case,Figure 2.8 c), the µ → eee branching ratio dom-inates in the allowed region of Ue3. As the LFV-mediating Higgs triplet boson does not couple toquarks, the µ → eee decay is enhanced comparedto the µ → eγ decay and the muon-to-electronconversion processes, which are both loop sup-pressed.

This enhancement of the LFV tree diagram isalso found to be large in extra dimension mod-els [48,90] or models with new heavy Z bosons. InRandall-Sundrum (RS) models [48], flavor chan-ging neutral currents (FCNCs) arise already at thetree level. This is caused by the flavor-dependentcouplings of these gauge bosons, due to their non-trivial profiles in the extra dimension. Moreover,FCNCs arise through the exchange of the Higgsboson, as due to the contribution to the fermionmasses from compactification, there is a misalign-ment between the masses and the Yukawa coup-lings.

Electroweak precision observables suggest thatfor RS models featuring the Standard Modelgauge group, the new-physics mass scale MKK

(the scale of the Kaluza Klein excitations) shouldnot be lower than O(10 TeV) at 99 % CL [91–93].Thus, without additional structure/symmetries,the experimental situation suggests that it couldbe challenging to find direct signals from RS mod-els at the LHC. In such a situation, precisionexperiments, like the measurement of the decayµ → eee, will furnish the only possibility to seethe impact of warped extra dimensions.

2.3 Theory Summary

The search for the decay µ → eee is in itself of fun-damental interest and might reveal surprises notforeseen by any of the models discussed above.This search is largely complementary to otherLFV searches, in particular to the decay µ → eγand to the µ → e conversion in muon captureexperiments. In a wide range of models for phys-ics beyond the standard model, highest sensitiv-ity in terms of branching ratio is expected for theµ → eee decay process.

12


Mu3eMu3e

Mu3e

Figure 2.8: Branching ratios of B(µ → eee), B(µ → eγ) and muon conversion B(µ → e) in different Higgstriplet scenarios with a degenerated, hierarchical or inverted mass hierarchy of the neutrinos as functionof the neutrino mixing matrix element Ue3 and for the model parameters: M = 200 GeV, A = 25 eV,and mν = 0.1 eV for the degenerate case. These plots were taken from [11] and the Ue3 constraints(green bands) as obtained from [19] were added posterior.

13

Chapter 3

Experimental Situation

3.1 SINDRUM Experiment

The SINDRUM experiment was in operation atPSI from 1983-86 to search for the process µ →eee. No signal was found and the limit B(µ →eee)< 10−12 was set at 90 % CL [15], assuming adecay model with a constant matrix element.

The main components of the experiment werea hollow double-cone shaped target of dimension58 × 220 mm2 to stop surface muons of 28 MeV/cin a solenoidal magnetic field of 0.33 T, five layersof multiwire proportional chambers and a triggerhodoscope. The main tracking parameters whichwere most relevant for the search sensitivity of theexperiment are shown in Table 3.1.

The time resolution obtained by the hodoscopeof less than 1 ns was, together with the achievedmomentum resolution, sufficient to suppress theaccidental background completely.

After all selection cuts, no candidate event wasseen by the SINDRUM experiment. The sensitiv-ity of the experiment was mainly determined bythe µ → eeeνν background process and estimatedas 5 · 10−14 [94]; the obtained limit was basicallygiven by the limited number of muon stops.

3.2 MEG Experiment

The MEG experiment at PSI is in operation since2008 and is searching for the LFV decay µ → eγ.The main components used for event reconstruc-tion are drift chambers for positron detection anda liquid xenon calorimeter for photon detection.

In the first running period in the year 2008about 1014 muons were stopped on target [24].No signal was found and a limit on the decay ofB(µ → eγ)< 2.8 · 10−11 (90 % C.L.) was set.

After upgrading the detector the search sensit-ivity and the limit was improved using data takenin the years 2009/2010 to B(µ → eγ)< 2.4 · 10−12

(90 % C.L.) [14].

The dominant background contribution for µ →eγ comes from accidentals where a high energyphoton from a radiative muon decay or froma bremsstrahlung process is recorded, overlayedwith a positron from the upper edge of the Michelspectrum. This accidental background mainly de-termines the final sensitivity of the experiment.

The amount of background is predominantly de-termined by the timing, tracking and energy resol-ution. Selected resolution parameters as achievedin the 2009 run are summarized in Table 3.2.The MEG experiment will continue operation un-til middle of 2013. The final sensitivity is expec-ted to be a few times 10−13. The collaborationhas started to discuss possible upgrades to fur-ther improve the sensitivity by about one order ofmagnitude. These numbers are to be compared tothe bound from the earlier MEGA experiment ofB(µ → eγ)< 1.2 · 10−11 [13].

The study of the µ → eγ decay sets stringentbounds on models predicting new heavy particlesmediating LFV dipole couplings. These dipolecouplings can also be tested in the process µ →eee, where the sensitivity is reduced by a factorof α

3π (ln(m2µ/m2

e) − 11/4) = 0.006 (note howeverthat for µ → eee also box diagrams, Z0-mediatedpenguin diagrams and tree digrams contribute as

14


SINDRUM parameter Value

rel. momentum resolution σp/p 5.1 % (p = 50 MeV/c)rel. momentum resolution σp/p 3.6 % (p = 20 MeV/c)polar angle σθ 28 mrad (p = 20 MeV/c)vertex resolution σdca ≈ 1 mmMWPC layer radiation length in X0 0.08 % - 0.17 %

Table 3.1: SINDRUM tracking parameters taken from [15].

described in chapter 2). In the case that the LFVdipole couplings are dominant, the projected sens-itivity of 10−13 of the MEG experiment corres-ponds accordingly to a sensitivity of about 10−15

in the search for the µ → eee decay and the en-visaged sensitivity of B(µ → eee) = 10−16 corres-ponds to more than one order of magnitude highersensitivity compared to the MEG experiment.

3.3 Muon Conversion Experiments

Muon to electron conversion experiments µ → eon nuclei exploit the clear signature of monochro-matic electrons. Differently to the search for LFVmuon decays, which are performed using DC anti-muon beams in order to reduce accidental back-grounds, muon conversion experiments are per-formed using pulsed muon beams to reduce therapidly decaying pion background. A limitationof this type of experiment is the background fromordinary decays of captured muons with large nuc-lear recoil and from pions.

The most stringent limits for muon-electronconversion on various nuclei have been obtainedby the SINDRUM II collaboration [16,97,98]. The

MEG parameter 2011 publ. Value

rel. momentum resolution σp/p 0.7 % (core)polar angle σθ 9 mradazimuthal angle σφ 7 mradradial vertex resolution σR 1.1 mmlong. vertex resolution : σZ 1.5 mm

Table 3.2: Best MEG tracking parameter resol-utions achieved in the year 2009/2010. The res-olutions are given for positrons of 53 MeV/c mo-mentum. Values taken from [14].

strongest limit has been set using a gold targetB(µ Au → e Au)< 7 · 10−13 [16].

Similar to the µ → eee process, the sensitivityto dipole couplings in muon conversion is reducedby about αem compared to the more direct µ →eγ search. However, new experiments plannedat Fermilab (Mu2e [46, 99, 100]) and at J-PARC(COMET [45,101,102] and PRISM [103,104]) aimfor branching ratios of 10−16 or smaller relativeto the captured muon decay and have a highersensitivity to LFV dipole couplings than the run-ning MEG experiment. Similar to the µ → eeeprocess, also four-fermion couplings are tested inµ → e conversion experiments. These couplingsinvolve light quarks and are thus complementaryto all other LFV search experiments.

The Mu2e and COMET experiments are ambi-tious projects and are expected to come into oper-ation at earliest by the end of this decade. In a fewyears time the DeeMe experiment at J-PARC [44]will start taking data, aiming for a sensitivity formuon-to-electron conversions of 10−14.

At Osaka university, the MuSIC project [105,106] aims for a very high intensity DC muon beamusing a high-field capture solenoid around a thickconversion target. One of many possible users ofthat beam is a µ → eee experiment. However, anexperimental concept has not yet been presented.

3.4 LFV in τ Decays

A wide variety of LFV decay channels are open inτ decays. These decay modes have been extens-ively explored at the B-factories, producing limitson branching ratios of a few 10−8, see Table 3.3and Figure 3.1. The next generation of B exper-iments at e+e− colliders could push these limitsdown by one to two orders of magnitude. For cer-tain channels such as τ → µµµ, the LHCb exper-

15


γ -e

γ - µ0 π -

e0 π - µη - eη - µ’η - e’η - µ

0 S K-

e0 S

K- µ0

f- e0

f- µ0ρ - e0ρ - µ K*

-e

K*

- µK

* - eK

* - µ

φ -e

φ - µω - eω - µ

- e+

e-e

- e+

e- µ- µ + µ -

e- µ + µ - µ-

e+ µ - e- µ +

e- µ- π + π -

e- π + π - µ-

K+ π -e

- K+ π - µ

- π + K- e

- π + K- µ

- K+

K- e-

K+ K- µ

0 S K

0 S K-

e0 S

K0 S

K- µ- π +

e- π- π + µ - π-

K+ e- π

- K+ µ - π

- K+

e-K

- K+ µ -

KΛ - πΛ - πΛ -

KΛ -

K

dec

ays

τ90

% C

.L. u

pper

lim

its fo

r LF

V

-810

-710

-610

-510

γl 0lP 0lS 0lV lll lhh hΛ

CLEOBaBarBelle

HFAG-TauWinter 2012

Figure 3.1: Limits on LFV τ decays. Taken from [95]

iment could also be competitive given the lumin-osity expected in the coming years [107,108].

3.5 LFV at the Large Hadron Col-

lider

LFV signatures might be observed at the LHCif e.g. supersymmetric particles are discovered,which naturally generate LFV couplings in sleptonmass mixing. Consequently, if sleptons are lightenough to be produced in pairs, different leptonflavors might show up in decay chains such as:ℓ+ℓ− → ℓ+ℓ−′χ0χ0.

Known and new scalar or vector particles couldalso have lepton violating tree couplings and mightbe directly reconstructed from resonance peaks:H → ℓℓ′ or Z ′ → ℓℓ′. Due to the existingbounds on flavor changing processes, these LFVdecays are small and difficult to detect above

the large background from WW -production withsubsequent leptonic decays. It seems however,that with high enough luminosities, the LHC cane.g. go beyond the LEP bounds [109–112] on LFVZ decays [113].

If new particles exist at the TeV mass scale,i.e. in the discovery reach of the LHC, it isvery likely that precision experiments will discoverlepton flavor violation via radiative loops. Dedic-ated LFV search experiments like the proposedµ → eee experiment would then allow one tomeasure the LFV couplings of the new particles,complementary to the TeV scale experiments atthe LHC.

Conversely, in the case that no new physics (ex-cluding the SM Higgs boson [114, 115]) were dis-covered at the LHC, the discovery of LFV in preci-sion experiments is not excluded as e.g. rare muondecays are testing the mass scale > 1 PeV, threeorders of magnitude higher than at LHC.

16


Decay Belle limit Babar limit Belle II proj. Belle II proj. SuperB proj.1

channel (5 ab−1) (50 ab−1) (75 ab−1)

τ → µγ 4.5 · 10−8 [26] 4.4 · 10−8 [27] 10 · 10−9 [42, 43] 3 · 10−9 [42, 43] 1.8 · 10−9 [96]τ → eγ 12 · 10−8 [26] 3.3 · 10−8 [27] 2.3 · 10−9 [96]τ → µµµ 2.1 · 10−8 [34] 3.3 · 10−8 [28] 3 · 10−9 [42, 43] 1 · 10−9 [42, 43] 2 · 10−10 [96]τ → eee 2.7 · 10−8 [34] 2.9 · 10−8 [28] 2 · 10−10 [96]τ → µη 2.3 · 10−8 [25] 15 · 10−8 [33] 5 · 10−9 [42, 43] 2 · 10−9 [42, 43] 4 · 10−10 [96]τ → eη 4.4 · 10−8 [25] 16 · 10−8 [33] 6 · 10−10 [96]τ → µK0

S 2.3 · 10−8 [35] 4.0 · 10−8 [31] 2 · 10−10 [96]τ → eK0

S 2.6 · 10−8 [35] 3.3 · 10−8 [31] 2 · 10−10 [96]

Table 3.3: Measured and projected limits on selected lepton flavour violating τ decays (90 % C.L.).1 The SuperB projections assumed a polarized electron beam; they also assumed that all backgrounds except initial state

radiation can be suppressed to the desired level. The SuperB project was canceled in November 2012.

17

Chapter 4

The Decay µ → eee

4.1 Kinematics

The decay µ → eee proceeds promptly. For dis-criminating signal and background, energy andmomentum conservation can be exploited. Thevectorial sum of all decay particle momenta shouldvanish:

|~ptot| =∣

∣

∣

∑

~pi

∣

∣

∣= 0 (4.1)

and the total energy has to be equal to the muonmass.

The energies of the decay electrons (positrons)are in the range (0 − 53) MeV. All decay particlesmust lie in a plane and the decay is describedby two independent variables in addition to threeglobal rotation angles, which describe the orient-ation in space.

4.2 Detector Acceptance

The acceptance of the proposed µ → eee exper-iment is determined by its geometrical accept-ance and energy coverage. For various couplingassumptions about the LFV amplitude, see alsoequation 2.1, the energy spectrum of the highestenergy, E1, and lowest energy decay particles,Ee

min, are shown in Figures 4.1 and 4.2, respect-ively. In order to achieve a high acceptance, thedetector must be able to reconstruct tracks withmomenta ranging from half the muon mass downto a few MeV with large solid angle coverage.The proposed experiment should cover the energyrange > 10 MeV to provide acceptances of 50 % ormore for all models.

Figure 4.1: Energy distribution of the highest en-ergy positron in the decay µ+ → e+e−e+ for dif-ferent effective LFV models. The solid red and thegreen lines correspond to pure four-fermion con-tact interaction models (no penguin) contribution.

4.3 Backgrounds

The final sensitivity of the proposed experimentdepends on the ability to reduce backgrounds fromvarious sources. Two categories of backgroundsare considered; irreducible backgrounds, such asµ+ → e+e+e−νν, which strongly depend on thegranularity and resolution of the detector, and ac-cidental backgrounds that scale linearly or withthe square of the beam intensity.

In the following sections, the main backgroundsources considered are discussed.

18


Figure 4.2: Acceptance of the lowest energy de-cay electron (positron) for different effective LFVmodels as function of the minimum transverse mo-mentum. The solid red and green lines correspondto pure four-fermion contact interaction models(no penguin) contribution.

4.3.1 Internal Conversions

The decay µ → eeeνν occurs with a branchingfraction of 3.4 · 10−5 [117]. It can be distinguishedfrom the µ → eee process by making use of en-ergy and momentum conservation to reconstructthe undetected neutrinos; in order to separate theµ → eee events from µ → eeeνν events, the totalmomentum in the event is required to be zero andthe energy equal to the muon rest energy. Thebranching fraction as a function of the energy cutof the µ → eeeνν process [116] is shown in Fig-ure 4.3. Figures. 4.4 and 4.5 show the energy spec-trum of all and the lowest energy electron frominternal conversion decays, Figs. 4.6 and 4.7 theinvariant masses of e+e− combinations calculatedwith the matrix element from [116]. This processis the most serious background for the µ → eeesearch and can only be resolved by a very goodenergy resolution.

4.3.2 Michel Decays

Using a beam of positive muons, one of themain processes contributing to accidental back-ground is that of the ordinary Michel decay µ+ →e+νν. This process does not produce a negat-ively charged particle (electron), which is one of

]2Visible Mass [MeV/c99 100 101 102 103 104 105

Inte

grat

ed b

ranc

hing

frac

tion

-2110

-2010

-1910

-1810

-1710

-1610

-1510

-1410

-1310

-1210 All internal conversion decays

All decay electrons in detector acceptance

Figure 4.3: Integrated branching fraction for thedecay µ → eeeνν in dependence of the visiblemass for all internal conversion decays and thosewith all three decay particles in the detector ac-ceptance. The matrix element was taken from[116].

Energy [MeV]-/e+e0 10 20 30 40 50

Pro

babi

lty p

er 1

00 K

eV

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

Figure 4.4: Spectrum of electrons from internalconversion decays.

[MeV]-/e+Lowest energy of e0 10 20 30 40 50

Pro

babi

lty p

er 1

00 K

eV

0

0.001

0.002

0.003

0.004

0.005

0.006

Figure 4.5: Spectrum of the electron with min-imum energy from internal conversion decays.

19


[MeV], large-e+em0 20 40 60 80 100

[MeV

], s

mal

l- e

+ em

0

10

20

30

40

50

60

70

80

0

5000

10000

15000

20000

25000

30000

35000

40000

Figure 4.6: Invariant masses of the two possiblee+e− combinations for internal conversion decays.

[MeV],large-e+em0 20 40 60 80 100

[MeV

],s

mal

l- e

+ em

0

10

20

30

40

50

60

70

80

0

0.002

0.004

0.006

0.008

0.01

Figure 4.7: Invariant masses of the two possiblee+e− combinations for internal conversion decayswith a visible mass above 90 MeV and the elec-trons and positrons in the detector acceptance(E > 10 MeV, | cos θ| < 0.8).

the main characteristics of the µ+ → e+e+e− de-cay, and can therefore only contribute as potentialbackground if a track is wrongly reconstructed.Other processes which “naturally” provide negat-ively charged tracks (electrons) are radiative de-cays with internal or external photon conversionsor Bhabha scattering.

4.3.3 Radiative Muon Decays

The process µ+ → e+γνν (branching fraction1.4 · 10−2 for photon energies above 10 MeV [117])can deliver an oppositely charged electron if thephoton converts either in the target region or in

the detector. Contributions from conversions out-side of the target are greatly suppressed if a vertexconstraint is applied and by minimizing the ma-terial in both the target and detector. Photonconversion in the target generates an event topo-logy similar to the radiative decay with internalconversion: µ → eeeνν, which is discussed above.

Due to the missing energy from the neutri-nos, this process mainly contributes to the acci-dental background in combination with an ordin-ary muon decay.

4.3.4 Bhabha Scattering

Positrons from the ordinary muon decay or beam-positrons can undergo Bhabha scattering withelectrons in the target material, leading to anelectron-positron pair from a common vertex. Dueto the missing energy, this process mainly contrib-utes to the accidental background in combinationwith an ordinary muon decay.

4.3.5 Pion decays

Certain decays of pions, especially π → eeeν(branching fraction 3.2 · 10−9 [117]) and π → µγν(branching fraction 2.0 · 10−4 [117]) with sub-sequent photon conversion are indistinguishablefrom signal events if the momenta of the finalstate particles fit the muon mass hypothesis; alow pion contamination of the primary beam (es-timated to be in the order of 10−12 for the highintensity beamline), the small branching fractionand the small slice of the momentum is assumedto lead to negligible rates in the kinematic regionof interest.

4.3.6 Summary of Background Sources

First simulation studies have been performed tocalculate the different background contributions.Their results indicate that purely accidental back-grounds for ∼ 109 muons stops per second aresmall for the proposed high resolution detector.

The main concern are irreducible backgrounds,such as the process µ → eeeνν, which can only bereduced by a very good tracking resolution result-ing in total energy resolution of σE < 1 MeV forthe aimed sensitivities < 10−15.

20

Part II

The Mu3e Experiment

21

Chapter 5

Requirements for Mu3e

5.1 Goals of the Experiment

The goal of the Mu3e experiment is to observe theprocess µ → eee if its branching fraction is largerthan 10−16 or otherwise to exclude a branchingfraction of > 10−16 at the 90 % certainty level.In order to achieve these goals, > 5.5 · 1016 muondecays have to be observed1 and any backgroundmimicking the signal process has to be suppressedto below the 10−16 level. The additional require-ment of achieving these goals within a reasonablemeasurement time of one year of data taking dic-tates a muon stopping rate of 2 · 109 Hz and a highgeometrical acceptance and efficiency of the exper-iment.

We plan to perform the experiment in twophases. The exploratory phase I will make useof existing muon beams at PSI and serve to com-mission the detectors, gain experience with thenew technologies and validate the experimentalconcept, whilst at the same time producing a com-petitive measurement. The goal for this first phaseis to reach a sensitivity of 10−15, thus pushingthe existing limit by three orders of magnitude.For this level of sensitivity, the demands on thedetector are somewhat relaxed, thus allowing forcross-checks between detectors also on analysislevel or running without the full instrumentation.The lower data rates also will not require the fullread-out and filter farm system. The second phaseof the experiment on the other hand will aim forthe ultimate sensitivity and thus require that thedetector works as specified and a new beamlinedelivers > 2 · 109 Hz of muons.

1Assuming a total efficiency of 30 %.

The expected rate at an existing beamline is1 − 1.5 · 108 Hz of muons on target. In order tohave a safety margin, we usually assume 2 · 108 Hzfor phase I background studies, except where therunning time is concerned.

This proposal discusses the phase I experi-ment in detail and shows the path leading to fullrate capability. We also discuss alternative ap-proaches.

5.2 Challenges for the Experiment

5.2.1 Backgrounds

There are two kinds of backgrounds: Overlays ofdifferent processes producing three tracks resem-bling a µ → eee decay (accidental background)and radiative decays with internal conversion (in-ternal conversion background) with a small energyfraction carried away by the neutrinos. Accidentalbackground has to be suppressed via vertexing,timing and momentum measurement, whereasmomentum measurement is the only handle on in-ternal conversion.

5.2.2 Geometric acceptance

For a three-body decay with a priori unknown kin-ematics such as µ → eee, the acceptance has tobe as high as possible in order to test new phys-ics in all regions of phase space. There are twokinds of acceptance losses, losses of tracks down-stream or upstream, where beam entry and exitprevent instrumentation, and losses of low trans-verse momentum tracks, which do not transverse

22


]2Reconstructed Mass Resolution [MeV/c0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

frac

tion

in s

igna

l reg

ion

νν e

ee→ µ -2010

-1910

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

5 sigma around signal





Figure 5.1: Contamination of the signal region(one sided cut) with internal conversion events asa function of momentum sum resolution.

a sufficient number of detector planes, and are notreconstructed.

5.2.3 Rate capability

The Mu3e detector should be capable of runningwith 2 · 109 Hz of muon decays. This poses chal-lenges for the detectors, the data acquisition andthe readout.

5.2.4 Momentum resolution

The momentum resolution directly determines towhat level internal conversion background can besuppressed and thus to which level the experimentcan be ran background free. In order to reach asensitivity of 10−16 with a 2σ cut on the recon-structed muon mass, the average momentum res-olution has to be better than 0.5 MeV. For thephase I experiment aiming at 10−15, this require-ment is relaxed to 0.7 MeV, see Figure 5.1.

5.2.5 Vertex resolution

Keeping apart vertices from different muon decaysis a key tool in suppressing accidental background.The vertex resolution is essentially determined bythe amount of multiple scattering (and thus ma-terial) in the innermost detector layer. Ideallythe vertex resolution is sufficient to eliminate al-most all combinatorial backgrounds; for the phaseI rates, this appears achievable, whereas in thephase II experiment, very good timing is neededin addition.

5.2.6 Timing resolution

Good timing is essential for reducing combinator-ial background at rates which lead to more thanabout 10 muon decays per frame on average.

23

Chapter 6

Experimental Concept

The Mu3e detector is aimed at the backgroundfree measurement or exclusion of the decay µ →eee at the level of 10−16. As discussed in moredetail in the preceding chapter 5, these goals re-quire to run at high muon decay rates, an excel-lent momentum resolution in order to suppressbackground from the internal conversion decayµ → eeeνν and good vertex and timing resolu-tion in order to efficiently suppress combinatorialbackground.

We intend to measure the momenta of the muondecay electrons in a solenoidal magnetic field us-ing a silicon pixel tracker. At the electron ener-gies of interest, multiple Coulomb scattering in de-tector material is the dominating factor affectingmomentum resolution. Minimizing this materialin the active detector parts is thus of utmost im-portance.

Figure 6.1: Tracking in the spatial resolution dom-inated regime

The proposed detector consists of an ultra thinsilicon pixel tracker, made possible by the High-Voltage Monolithic Active Pixel (HV-MAPS)technology (see chapter 10). Just four radial lay-ers around a fixed target in a solenoidal magneticfield allow for precise momentum and vertex de-termination. Two timing detector systems guar-antee good combinatorial background suppressionand high rate capabilities.

The Mu3e experiment is designed to have asensitivity four orders of magnitude better thanthe current limit on µ → eee (10−12), so it is reas-onable to plan for a staged detector design, witheach stage roughly corresponding to an order ofmagnitude improvement.

Figure 6.2: Tracking in the scattering dominatedregime

24


6.1 Momentum Measurement with

Recurlers

Due to the low momenta of the electrons frommuon decay, multiple scattering is the dominat-ing effect on momentum measurement. With ourfine-grained pixel detector, we are thus in a regimewhere scattering effects dominate over sensor res-olution effects, see Figs. 6.1 and 6.2. Thus addingadditional measurement points does not necessar-ily improve the precision.

The precision of a momentum measurement de-pends on the amount of track deflection Ω in themagnetic field B and the multiple scattering angleΘMS , see Figure 6.3; to first order:

σp

p∝ ΘMS

Ω. (6.1)

So in order to have a high momentum precision,a large lever arm is needed. This can be achievedby moving tracking stations to large radii, whichhowever compromises the acceptance for low mo-mentum particles. In the case of muon decays, alltrack momenta are below 53 MeV and all trackswill thus curl back towards the magnet axis ifthe magnet bore is sufficiently large. After ex-actly half a turn, effects of multiple scattering onmomentum measurement cancel in first order, seeFigure 6.4. To exploit this feature we optimizedthe experimental design specifically for the meas-urement of re-curling tracks, leading to a narrow,long tube layout.

Measuring the momentum from bending outsideof the tracker also allows us to place timing de-tectors inside, without strongly affecting the res-olution.

6.2 Baseline Design

The proposed Mu3e detector is based on twodouble layers of HV-MAPS around a hollowdouble cone target, see Figures 6.5 and 6.6. Theouter two pixel sensor layers are extended up-stream and downstream to provide precise mo-mentum measurements in an extended region withthe help of re-curling electrons. The silicon de-tector layers (described in detail in chapter 10)are supplemented by two timing systems, a scin-tillating fibre tracker in the central part (seechapter 11) and scintillating tiles (chapter 12) in-side the recurl layers. Precise timing of all tracks

Ω

MS

θMS

B

Figure 6.3: Multiple scattering as seen in the planetransverse to the magnetic field direction.

Ω ~ π

MS

θMS

B

Figure 6.4: Multiple scattering for a semi-circulartrajectory.

25


is necessary for event building and to suppress ac-cidental combinatorial background.

The entire detector is built in a cylindricalshape around a beam pipe, with a total length ofapproximately 2 m, inside a 1 T solenoid magnetwith 1 m inside diameter and 2.5 m total length(chapter 8). In the longitudinal direction the de-tector is sub-divided into five stations, the centraldetector with target, inner silicon double layer,fibre tracker and outer silicon double layer, andtwo forward and backward recurl stations withtwo silicon recurl layers surrounding a tile tim-ing detector. In order to separate tracks comingfrom different muon decays, the target has a largesurface with 10 cm length and 2 cm diameter. Thetarget shape is a hollow double cone, see chapter9. Around the target the two inner silicon pixellayers, also referred to as the vertex layers, covera length of 12 cm. The innermost layer will have12, the second one 18 sides of 1 cm each, corres-ponding to an average radius of 1.9 cm and 2.9 cm,respectively. The inner silicon layers are suppor-ted by two half cylinders made from 25 µm thinKapton foil mounted on plastic end pieces. Allsilicon sensors are thinned to 50 µm, resulting in aradiation length of X/X0 ≤ 0.1 % per layer. Thedetector will be cooled with gaseous helium.

The hit information from the silicon sensors isread out at a rate of 20 MHz using timestampsproviding a time resolution of 20 ns.

The fibre tracker sits inside silicon pixel layerthree at around 6 cm, providing timing informa-tion for decay positrons and electrons. It is com-posed from three to five layers of 250 µm thick36 cm long scintillating fibres, see Figure 6.6. Thefibre tracker is read out by fast silicon photo mul-tipliers and can provide timing information with≤ 1 ns accuracy.

The silicon pixel layers three and four are justoutside the fibre tracker at a mean radius of 7.6 cmand 8.9 cm. The active area has a cylindricalshape of 36 cm length. The layer three has 24sides, layer four 28 sides of 1.9 cm width each.Both outer layers are constructed as modules of 4sides, six modules for layer three and seven mod-ules for layer four. Similar to the inner two layersthe mechanical frames of these modules are buildfrom 25 µm Kapton foil with plastic end pieces.

Copies of silicon pixel layer three and four arealso used in the recurl stations. Two recurl sta-tions each are covering the upstream and down-stream regions. These recurl stations add fur-

ther precision to the momentum measurement ofthe electrons, see section 6.1. While the siliconlayer design is (almost) identical to the centralpart, the timing detector in the recurl region canbe much thicker compared to the fibre tracker,as the particles can and should be stopped here.This is done by using scintillating tiles of about7.5 × 7.5 × 5 mm3 size. These tiles provide a muchbetter time resolution than the thin fibre trackerin the center. Following the dimensions of therecurl silicon layers, the tile station have a act-ive length of 36 cm and a cylindrical shape witha radius of ≈ 6 cm. All central detector com-ponents are mounted on spokes providing a lightstiff support. The recurl silicon layers and tilesare mounted on the beam pipe support. In addi-tion to the silicon and scintillating tile sensors thebeam pipe support also carries the services andthe PCBs equipped with the front-end electronics(chapter 13). Signal and power connection to thesilicon layers is provided by flex prints which arealso part of the mechanical support of the siliconsensors.

6.3 Building up the Experiment

One of the advantages of the design conceptpresented is its modularity. Even with a par-tial detector, physics runs can be taken. Thefull instrumentation is only required for achievingthe final sensitivity of 10−16 at muon rates above1 · 109 Hz. On the other hand, in an early commis-sioning phase at smaller muon stopping rates, thedetector could run with the central silicon detectoronly (see Figure 6.7). The silicon detectors of therecurl stations are essentially copies of the centralouter silicon detector; after a successful commis-sioning of the latter, they can be produced andadded to the experiment as they become avail-able together with the connected tile detectors.The fibre tracker can also be added later, sinceit is only needed to resolve combinatorial back-ground at higher event rates and track multiplicit-ies. The loss of momentum resolution due to mul-tiple scattering at the additional material of thefibre tracker will be fully compensated by the im-proved momentum measurement with re-curlers.The configuration with two recurl stations (Fig-ure 6.8) defines a medium-size setup, well suitedfor phase I running. The configuration with four

26


Target

Inner pixel layers

Scintillating bres

Outer pixel layers

Recurl pixel layers

Scintillator tiles

μ Beam

Figure 6.5: Schematic view of the experiment cut along the beam axis in the phase II configuration.

Figure 6.6: Schematic view of the experiment cut transverse to the beam axis. Note that the fibres arenot drawn to scale.

recurl stations (Figure 6.9) defines the full setupfor phase II running.

In the following sections, the experimental con-figurations for running at the existing πE5 beam-line (the Phase I Experiment) and the final de-tector for running at > 1 · 109 Hz muon stoppingrate (the Phase II Experiment) are outlined.

6.4 The Phase I Experiment

The phase I of the Mu3e experiment will start witha minimum configuration (phase IA detector) withthe target regions surrounded by double layers ofinner and outer silicon pixel detectors, see Figure6.7. This configuration defines the minimal config-uration as it allows to determine the momentum,the vertex position and the time of the decay pre-

27


Target

Inner pixel layers

Outer pixel layers

μ Beam

Figure 6.7: Minimum detector cofiguration for early commissioning with central silicon only (phase IA).

Target

Inner pixel layers

Scintillating bres

Outer pixel layers

Recurl pixel layers

Scintillator tiles

μ Beam

Figure 6.8: Detector with one set of recurl stations for physics runs and tile detector commissioning(phase IB).

Target

Inner pixel layers

Scintillating bres

Outer pixel layers

Recurl pixel layers

Scintillator tiles

μ Beam

Figure 6.9: Final detector with two sets of recurl stations for high intensity physics runs (phase II).

28


cise enough to produce very competitive physicsresults with a sensitivity down to O(10−14). It isforeseen to run in the first year in this configura-tion at a muon stopping rate on target at around2 · 107 Hz. The number of decays in one readoutframe of the pixel tracker of 50 ns will be aroundone on average and combinatorial background canbe suppressed with the help of the vertex recon-struction. The precision of the momentum res-olution will be somewhat limited, as most tracksdo not recurl within the instrumented volume, seechapter 17.

In the phase IB the detector will be complemen-ted by the first pair of recurl stations, the corres-ponding tile detectors and the fibre tracker, seeFigure 6.8. Adding the recurl stations will sig-nificantly enhance the momentum resolution andthus improve the suppression of internal conver-sion background. The insertion of the fibre trackerand the tile detector stations gives a much bettertime resolution in comparison to the silicon pixelonly. The fibre tracker will deliver a time resol-ution of about 200-300 ps, while the tile detectorwill have < 100 ps resolution for the tracks passingthe recurl stations. The high time resolution will

allow running at the highest possible rate at theπE5 muon beam line at PSI of ≈ 1 · 108 Hz. Thesensitivity reach in this phase of the experiment ofO(10−15) will be limited by statistics only. limitedby the available muon decay rate.

6.5 The Phase II Experiment

A new high intensity muon beam line [118] deliver-ing ≈ 2 · 109 Hz muon stops is crucial for the phaseII of the proposed experiment. To fully exploit thenew beam facility the limited detector acceptanceat phase IB will be further enhanced by addinganother a second pair of recurl and tile detectorstations, see Figure 6.9. These extra stations willallow to measure precisely the momentum of allparticles in the acceptance of the inner trackingdetector. At the same time the extra tile detectorstations with their high time resolution and smalloccupancy will help to fight the increased com-binatorics at very high decay rates. The com-bined performance of the final detector setup to-gether with the high stopping rate will allow tosearch for the µ → eee decay with a sensitivity ofB(µ → eee)≤ 10−16.

29

Chapter 7

Muon Beam

7.1 General Beam Requirements

The general beam requirements for a high intens-ity, low-energy, stopped muon coincidence exper-iment such as Mu3e are six-fold: an abundantsupply of low-energy surface muons (from stoppedpion decay at rest, at the surface of the produc-tion target [119]) capable of being stopped in athin target; high transmission optics at 28 MeV/c,close to the kinematic-edge of stopped pion de-cay and hence close to the maximum productionrate of such muons, as shown in Figure 7.1; asmall beam emittance to minimize the stopping-target diameter; a momentum-byte of less than

4000

3500

3000

2500

2000

1500

1000

500

0

No

rma

lize

d R

ate

Z- Branch Momentum Spectrum

25 26 27 28 29 30 31 32 33Muon Momentum [MeV/c]

Figure 7.1: πE5 measured muon momentum spec-trum with fully open slits. Each point is obtainedby optimizing the whole beam line for the cor-responding central momentum and measuring thefull beam-spot intensity. The red-line is a fit tothe data, based on a theoretical p3.5 behaviour,folded with a Gaussian resolution function corres-ponding to the momentum-byte plus a constantcloud-muon background.

10 % with an achromatic final focus, allowing analmost monochromatic beam with a high stoppingdensity, to be stopped in a minimally thick tar-get; minimization and separation of beam-relatedbackgrounds such as beam e+ originating from π0-decay in the production target, or decay particlesproduced along the beam line and finally minim-ization of material interactions in the beam, forexample such as those in windows, thus requir-ing vacuum or helium environments to keep themultiple scattering under control.

7.2 Beam for phase I running

As previously outlined, a multi-staged detectorconfiguration will be sought for phase I running,this in turn requires muon beam intensities ran-ging between (107-108) muons/s for the initialphase IA (central detectors), while for phase IBa maximal intensity close to 1 · 108 muons/s willbe sought. The quoted maximum beam intens-ity which includes a phase space reduction factordue to collimation in the central region of theMu3 magnet is based on measured intensities atthe centre of the MEG detector, without a de-grader and normalized to a proton beam currentof 2.3 mA. This demand for the highest intensitiesnecessitates the selection of only one possible facil-ity in the world, namely the πE5 channel at PSI.Based on the experience gained in the design of theMEG beam line, a similarly developed concept isalso envisaged for phase I of Mu3e. This shouldallow the required muon intensity to be achieved.However, since the area is likely to be shared with

30


T r i p l e t I IQS K

QS K

QS K

T r i p l e t I I

T r i p l e t I IQS B

QS B

QS B

T r i p l e t I

S e p a r a t o r

C o l l i m a t o r

S y s t e m

p E 5 C h a n n e l

Proton Beam

" U " - C h a n n e l

" Z " - C h a n n e l

QSF 41

HSC 41

QSF 42

QSF 43

HSC 42

HSC 43

HSC 44

QSF 44

QSF 45

QSF 46

QSF 47

QSF 48

AST 41

ASC 41

KSF 41

FS 42

VSD 41

FS 43

FS 41

KD 42

KD 41

AHSW 41

M u 3 e

S o l e n o i d

C o u p l i n g

S o l e n o i d

p E 5 F r o n t A r e a

M u 3 e P h a s e I S c h e m a t i c

Figure 7.2: Mu3e potential beam line layout in the front-part of the πE5 area.

5000

4000

3000

2000

1000

0

No

rma

lize

d R

ate

Beam e+

Separator Scan

μ+

0-500 500 1000 1500 2000 2500Separator DAC value

Figure 7.3: Separator scan plot, measured postcollimator system. The black dots represent on-axis, low-threshold intensity measurements at agiven separator magnetic field value during thescan, for a fixed electric field value of −195 kV.The red curve represents a double Gaussian fit tothe data points, with a constant background. Aseparation of 8.1 muon beam σµ is found, corres-ponding to more than 12 cm separation of beam-spot centres at the collimator.

other experiments, that of MEG (R-99-05), andthe Lamb-shift experiment (R-98-03) a compactmuon beam line designed specifically to fit intothe front-part of the πE5 area is under design.This would not only allow the beam line elements,such as the Wien-filter, triplet I and II, plus theMEG collimator system to be used by this exper-iment, but would also allow access to the MEGdetector during running periods, by means of pla-cing a shielding wall just upstream of the MEGdetector, as previously adopted during the runperiods of experiment R98-03.

Figure 7.2 shows the potential area layout adop-ted. Surface muons of 28 MeV/c will be extractedfrom the πE5 “Z-channel” and the initial part ofthe current MEG beam line, including: TripletI, the 200 kV crossed-field Wien-filter, Triplet IIand the collimator system. This combination ofelements allows for an optimal beam correlatedbackground suppression, as demonstrated in Fig-ure 7.3, which shows the separation quality postcollimator, between muons and beam positrons forthe above mentioned section of beam line. Due tothe severe restrictions imposed by space, a match-ing section, including two dipole magnets of 90

and 66 bending angles respectively, with an in-termediate quadrupole doublet or triplet, is en-

31


visaged. A final doublet/triplet or intermediatetransport solenoid would in turn couple the beamline to the Mu3e superconducting magnet. Thebeam line vacuum is currently planned to endclose to the centre of the target and includes col-limation to match the beam-spot to the target sizeand prevent beam interactions from occurring dir-ectly in the small radii inner silicon layers. Theexpected usable muon intensity at the Mu3e tar-get is between 0.7-1.0 · 108 muons/s.

Although it is understood that simultaneousrunning of prospective πE5 experiments is notpossible, it is nevertheless clear that the Mu3ephase I beam line will in fact benefit from theavailability of MEG beam elements upstream ofthe detector and that this option, together withprovision of the available standard PSI magnetscurrently in storage or potentially sharable, wouldcover most of the beam line requirements, exceptthat of a short coupling solenoid, for which a po-tential solution is also currently under study andpossible dipole vacuum chamber modifications.

7.3 High intensity muon beamline

for phase II running

In order to reach the ultimate sensitivity goalof O(10−16) for the phase II experiment, an un-pulsed muon stopping rate in the GHz region isrequired. As demonstrated in Table 7.1, thereare no such (pulsed or unpulsed) high-intensitysources of muons currently available world-wide.Future intensity frontier facilities are however inthe planning in the US and Japan and are alsoassociated with LFV-experiments, more specific-ally Mu2e and Project X in the U.S. [46, 99] andthe COMET and PRIME/PRISM experiments inJapan [45, 101]. To meet the needs of such ex-periments a totally new concept is therefore ne-cessary. One such concept, which is still in itsinfancy, though is proving to be a promising can-didate, is the HiMB project at PSI [118], a next-generation high-intensity muon beam, currentlyunder study. A detailed feasibility study is due tostart at PSI in 2013. This concept would providethe basis for a new Mu3e beam line for the phase IImeasurements, based on the production of surfacemuons from the Swiss Spallation Neutron Source’s(SINQ) spallation target window.

The layout of the source in the SINQ hall [120],together with a schematic diagram of the source

with the proton beam injected from below isshown in Figure 7.4. The characteristics of thesource, which resembles a medium-flux reactor,are that the protons are injected from below anddefocussed onto a double-layered aluminium win-dow separated by a D2O cooling layer, before be-ing stopped in the target, a “cannelloni” constructof lead-filled zircaloy tubes.

The HiMB project plans to extract the down-ward travelling muons produced in the aluminiumwindow via a two-stage channel, the first stage,a solenoidal one, which uses the same beam-tube as the upward travelling protons and ex-tracts the muons, in the opposite direction, to alarge collection solenoid connecting to the secondstage, a conventional dipole and quadrupole chan-nel planned for the empty service cellar under theSINQ target. The general layout of both the pro-ton channel and the service area are shown in Fig-ure 7.5

There are several advantages of this concept,which would lead to a substantial enhancementcompared to target E, namely: the increased num-ber of primary proton interactions since 70 % ofthe beam stops in the target; a much larger pionenergy range of up to 150 MeV can be exploitedin the case of SINQ, above which the high en-ergy tail of the pion production cross-sections be-comes negligible, in the case of Target E this limitis around 45 MeV [121,122]; a substantially largerpion-production volume contribution compared toTarget E and finally a significantly larger surfacemuon production volume.

Realistic Monte-Carlo studies were undertakentogether with M. Wohlmuther (Head of the TargetDevelopment Group at PSI) using the Los AlamosLaboratory MCNPX code (Monte Carlo n-particleextended code), used also to design the SINQ tar-get. A simulation of the surface muon produc-tion rate was made using the complete model ofthe SINQ target environment. Based on a totalof 4 · 108 generated upward moving protons, cor-responding to the measured 2D beam profile atSINQ, a complete particle tracking was done us-ing three different event generators. For surfacemuons, the simulated fluences were determined forthe conditions of a particle leaving the target withthe correct energy, travelling downwards withinthe beam-pipe and crossing a horizontal plane25 cm below the window. This is shown schemat-ically in Figure 7.6. The calculated fluences fromthe three event generators agreed to within 35 %

32


Helium

supplyHelium

refrigerator

Vertical cutout

SINQ target blockD2 Con-

denser

cold

helium

~ 25 K

D2 System

D2 s

tora

ge

tan

k

vert

ica

l plu

g

horizontal plug D2D

2O

Re!ector

cold

moderator

Target

Beam

window

D2O

Moderator

H2ORe!ector

Neutron

beam tubes

Beam shutter

Neutron beam ports

Proton beam channel

Targetblock shielding

(steel & concrete)

Pro

ton

be

am

Neutron beam

Sample

Instrument

Floor

Target plug

Target enclosure

cooling system

Target cooling system

Moderator cooling system

Cooling

plant room

secondary

cooling loop

Figure 7.4: (Right) The SINQ spallation neutron source as seen in the experimental hall. The towerin the foreground, shown in section with the proton beam incident from below. (left) contains themain neutronics components, the spallation source, a Pb/Zr/Al structure cooled using D2O, the D2Omoderator tank and reflector shield and a cold-source of solid deuterium. The upper-part of the towerdeals with the cryogenic connections of the source.

Protons

Muons

SINQ Target Neutra Area

Access

Shaft

Muon Beam Cellar

Access

Shaft

Figure 7.5: Shows the layout of the proton beam line at SINQ as well as showing the possibility forextracting the muons into the empty cellar region below the SINQ target. The blue elements are dipolebending magnets and the red elements focussing quadrupole magnets. Since the proton and muons arelike-sign charged particles but travelling in opposite directions they will be bent in opposite directions,allowing the muons to access the empty cellar region shown. This is where a muon beam line could beplaced.

33


Laboratory/ Energy/ Present Surface Future estimatedBeam line Power µ+ rate (Hz) µ+/µ− rate (Hz)

PSI (CH) (590 MeV, 1.3 MW, DC)LEMS " 4 · 108

πE5 " 1.6 · 108

HiMB (590 MeV, 1 MW, DC) 4 · 1010(µ+)

J-PARC (JP) (3 GeV, 1 MW, Pulsed)currently 210 KW

MUSE D-line " 3 · 107

MUSE U-line " 2 · 108(µ+) (2012)COMET (8 GeV, 56 kW, Pulsed) 1011(µ−) (2019/20)PRIME/PRISM (8 GeV, 300 kW, Pulsed) 1011−12(µ−) (> 2020)

FNAL (USA)Mu2e (8 GeV, 25 kW, Pulsed) 5 · 1010(µ−) (2019/20)Project X Mu2e (3 GeV, 750 kW, Pulsed) 2 · 1012(µ−) (> 2022)

TRIUMF (CA) (500 MeV, 75 kW, DC)M20 " 2 · 106

KEK (JP) (500 MeV, 2.5 kW, Pulsed)Dai Omega " 4 · 105

RAL -ISIS (UK) (800 MeV, 160 kW, Pulsed)RIKEN-RAL 1.5 · 106

RCNP Osaka Univ. (JP) (400 MeV, 400 W, Pulsed)MUSIC currently max 4W 108(µ+) (2012)

means > 1011 per MW

DUBNA (RU) (660 MeV, 1.65 kW, Pulsed)Phasatron Ch:I-III 3 · 104

Table 7.1: Currently running muon beam facilities around the world used for particle physics experimentsand materials science µSR investigations. Also shown are the planned next-generation facilities designedfor cLFV experiments, together with an estimate of the starting date. The PSI HiMB solution is currentlyonly under study and is included purely for completeness.

of each other. Based on the standard event gener-ator, which also has the smallest statistical uncer-tainty, a summed fluence (E6 4.12 MeV) of surfaceand sub-surface muons of 1 · 1011 muons/s is cal-culated at a proton current of 3 mA on target E,which corresponds to 2.1 mA on SINQ. However,on the assumption that the proton current on Tar-get E will only rise to a maximum of 2.4 mA inthe future, a value that has already been achievedduring routine test periods since 2010 and takinginto account the variation of event generators inthe simulation, a conservative estimated fluenceof (3 ± 1) · 1010 good surface muons within a 10 %

FWHM momentum-byte could clearly be extrac-ted from the SINQ target (c.f. Table 7.2).

Conclusions seen from the source point of viewlook very promising and providing the beam canindeed be transmitted without significant losses,the phase II rates of 2 GHz muons could be real-ized. Finally, the current extraction principle,to be studied extensively in the feasibility study,is demonstrated in Figure 7.7. Muons originat-ing from the target window are to be guided ina downward direction using a low-field guidingsolenoid. Since the muon momentum is about afactor of 42 times smaller than that of the protons,the low-field for the muons should not dramat-

34


Pb + Zr + D2O

Vacuum

Al

D2O

25

cm

Figure 7.6: The Monte-Carlo model for the SINQtarget with all components taken into account.Light grey is the aluminium window, with theD2O cooling channel in the middle. Protons aregenerated according to a measured 2-D distribu-tion at the dark red plane. Surface muons leav-ing the target at the correct energy and cross-ing the light-green plane, 25 cm below the windowand moving downwards within the beam-pipe, arecounted.

P0 ∆P/P RateMeV/c % FWHM Hz

28 Full (7 ± 1) · 1010

28 10 (3 ± 1) · 1010

26 10 (3 ± 1) · 1010

Table 7.2: Estimated surface and sub-surfacemuon rates based on a proton current of 2.4 mAon Target E and full transmission efficiency.

Guiding solenoid

Solenoid

Fan-coupling

Vacuum chamber

Collection

solenoid

Figure 7.7: Schematic of HiMB muon extractionprinciple, with a guiding solenoid, followed by a fo-cussing solenoid to satisfy proton and muon trans-mission. The extraction is done in the fringe-fieldof the AHO magnet, with a strong-focussing col-lection solenoid. This is followed by a conventionalbeam line consisting of a dipole magnet and quad-rupole channel.

ically affect the protons. The present radiation-hardened, defocusing quadrupoles QTH 31 and32, just below the SINQ target, must be replacedby a rotationally symmetric element such as asolenoid, since the muons will not traverse a setof quadrupoles which only focus alternately inthe horizontal and vertical planes but have fieldstrengths that are 42 times too high for the muons.The extraction will be done in the fringe-field ofthe last dipole magnet AHO, which means thatthe following strong-focussing collection solenoidmust be placed close to the “fan-coupling” in or-der to fully collect the beam. Following this solen-oid is a dipole magnet whose function is to bendthe beam onto the horizontal plane, where a con-ventional secondary beam line quadrupole chan-nel could be constructed. As the current cellarends within just a few meters of the above SINQhall wall, one could envisage bending the beamupwards again at the end of the cellar and ex-tracting to a hall, exterior to SINQ, on the East-side. This would imply a relatively long beam lineof order (30-35) m, which is not too problematicfrom the muon loss (decay-in-flight) point-of-viewwhere 80 % transmission for 28 MeV/c muons is

35


Figure 7.8: Survival probability for muons at the kinematic edge of 29.79 MeV/c (green curve ), surfacemuons of 28 MeV/c (blue curve) and sub-surface muons of 25 MeV/c (red curve). Also shown (orangecurve) is the survival probability for pion contamination at 28 MeV/c, which is at the 10−12 level.

expected at 40 m, as shown in Figure 7.8. Alsoshown are similar plots for the maximum mo-mentum at the kinematic edge of pion-decay, aswell as for a lower momentum sub-surface muonbeam. Finally, the beam would naturally be freeof pion contamination to a level of about 10−12,which is also important for backgrounds relevantto the µ → eee decay such as π → eeeν andπ → µνγ.

The HiMB project is in its infancy at presentand there are many aspects that will be studiedin detail within the scope of the planned feasib-ility study, to show the feasibility of this next

generation high-intensity beam line. The initialstep taken concerning the muon source intensity,the basis for the HiMB feasibility study, has beenshown to be very promising. The next major stepsto be studied are the optical extraction of themuons from the proton beam and the solenoidalreplacement of the final proton defocussing quad-rupole doublet in front of the SINQ target, whilestill maintaining the safety restraints on the SINQtarget. The implementation of such a concept intothe SINQ environment could only coincide with amajor SINQ shutdown, which is currently plannedfor the period of 2016-2017.

36

Chapter 8

Magnet

The magnet for the Mu3e experiment has toprovide a homogeneous solenoidal magnetic fieldfor the precise momentum determination of themuon decay products. In addition it will also serveas beam optical element guiding the muon beamto the target. The basic parameters of the super-conducting solenoid magnet, which are currentlybeing specified for the preparation of order place-ments, are given in Table 8.1. The outer dimen-sions include also an iron field shield.

The nominal magnetic field strength is 1 T inthe central part, providing the optimum bendingradius in terms of resolution for the proposed ex-perimental design. A higher magnetic field wouldlead to a loss of acceptance as the low momentumparticles would not reach the central outer pixellayers (see Figure 8.1). A lower magnetic fieldwould lead to less magnetic deflection at constantmultiple scattering, leading to worse momentumresolution (see Figure 8.2). For systematic studiesand to allow for possible reuses of the magnet forother experimental measurements, the field can bevaried between 0.8 and 2 T.

The dimensions of the cylindrical warm boreof the magnet are 1 m in diameter and > 2 min length. The minimum diameter is given byfour times the bending radius of the highest mo-mentum (53 MeV/c) decay products at the lowestpossible field of B = 0.8 T plus the target dia-meter. In addition the detector support and ex-traction rail system has to be taken into accountwhen choosing the warm bore diameter.

The total length is a compromise between geo-metric acceptance for recurling particles and thevery tight space constraints for the phase I exper-

imental area at πE5. In principle a longer solen-oidal magnet would provide an intrinsically morehomogenous field. At both ends of the magnet it isforeseen to have full access by means of removableflanges.

While the ideal magnet would have a constantfield throughout the inner volume, real solenoidmagnets show a drop in field to 50 % at the endof the coil. The simplest solution would be alonger magnet, which however does not fit insidethe phase I area. Another possibility is to intro-duce correction coils at both ends of the magnet,such that the high field region can be extended.The insertion of several compensating coils wouldmake the magnet system more complex both inconstruction and operation due to the need of ad-ditional current settings and power supplies. Atpresent the baseline magnet concept foresees threeequal coils with a single power supply. The fieldchange along the z-axis has to be taken into ac-count for the reconstruction of tracks in the recurl

Magnet parameter Value

field for experiment 1 Tfield range 0.8 < 1 < 2 Twarm bore diameter 1 mwarm bore length > 2 mfield description ∆B/B ≤ 10−4

field stability ∆B/B (100 days) ≤ 10−4

outer dimensions: length < 2.5 mwidth < 2.5 mheight < 3.5 m

Table 8.1: Properties of the Mu3e magnet

37


Track transverse momentum [MeV/c]10 15 20 25 30 35 40 45 50

Effi

cien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.8 T

1.0 T

1.2 T

1.5 T

Figure 8.1: Reconstruction efficiency as a functionof track transverse momentum for different mag-netic fields, with recurl stations and without fibredetector.

Track momentum [MeV/c]0 10 20 30 40 50 60

Mom

entu

m r

esol

utio

n [M

eV/c

]

0

0.1

0.2

0.3

0.4

0.5

0.60.8 T

1.0 T

1.2 T

1.5 T

Figure 8.2: Momentum resolution as a functionof track momentum for different magnetic fields,with recurl stations and without fibre detector.

stations by using a look up table for the field mapplus interpolation between these points. Choos-ing the right granularity for the look-up table alinear interpolation of the field will be enough toreach an approximation of ∆B/B ≤ 10−4. Forthe fast online selection of events the assumptionof a constant field in the active part of the exper-iment will be sufficient. Though the assumption

of a constant (maximum) field leads to an system-atic bias towards larger momenta and an increaseof online selected background events from internalradiative muon decays with internal conversions,no signal events would be lost.

The superconducting magnet is made fromthree coils of equal size, which has advantages overone long coil in terms of mechanical stability. Thesmall dips in the magnetic field can be treatednumerically in the same way as the roll-off of thefield to the ends of the magnet. The choice forthe superconducting wires or conductors will bedriven by commercial availability, since standardcomponents allow for the desired 2 T maximumfield strength. A warm normal conducting mag-net is no option because of size, cost (copper price)and operational stability. Superconducting mag-nets have an intrinsic immunity against absolutefield changes, as they have to run at a constant(low) temperature. If feasible in terms of numberof cooling compressors, a dry cooled system willbe chosen.

There will be a magnetic shielding around themagnet. The shielding is required since the experi-mental hall is densely populated with other exper-iments and infrastructure. Also for the read-out ofthe proposed experiment it will be much easier towork in a low field environment. A beneficial sideeffect of the shielding is a gain of field homogen-eity inside the magnet and less field dependenceon variation of outside parameters.

The long term stability of the magnetic fieldshould be ∆B/B ≤ 10−4 over each 100 day datataking period. This can be achieved by using stateof the art magnet power supplies and by perman-ent measurement of the absolute field with a hallprobe inside the experiment.

The cool-down time for a system of the projec-ted size will be one week and the ramp time will bein the order of one hour. The number and power ofthe dry compressors will be chosen to fulfill theserequirements, in the case of a dry cooled magnet.

The D0 Magnet [123] fulfills most requirementsof the future Mu3e magnet and serves as a proto-type for the magnet design process.

38

Chapter 9

Stopping Target

The main challenge for the design of the stop-ping target is to optimize the stopping power onone hand and to minimize the impact on the trackmeasurement on the other hand. Therefore thestopping target should contain just enough ma-terial in the beam direction to stop most of the29 MeV surface muons but should be as thin aspossible in the flight direction of decay electronsmeasrued in the detector acceptance. Usage of alow Z material is advantageous as tails from largeangle Coulomb scatterering are suppressed. In ad-dition, the decay vertices should be spread out aswidely as possible in order to reduce accidental co-incidences of track vertices and to produce a moreor less even occupancy in the innermost detectorlayer.

9.1 Baseline Aluminium Design

100 mm

20

mm

10 mm

11.3°

30 μm Al 80 μm Al

A = 3204 mm2

Figure 9.1: Dimensions of the baseline design tar-get. Note that the material thickness is not toscale.

These requirements can be met by a hollowdouble cone target à la SINDRUM [15,94]. In ourbaseline design (see Figure 9.1), the target is madefrom 30 µm of aluminium in the front part and80 µm aluminium in the back part, with a totallength of 100 mm and a radius of 10 mm. This res-ults in an total area of 3204 mm2 and an effectivetarget thickness in beam direction of 560 µm cor-responding to 0.063 radiation lengths X0 of Alu-minium. The target can be suspended from theinnermost tracking layer by e.g. nylon fishing wire(which we assume in the simulation) and whichdoes not significantly add material in the beamline.

In the Geant4 [124] simulation (see 15), about83.3% of the muons1 that reach the target arestopped. Obviously, this fraction can be increasedby adding material, which will however lead toadditional multiple scattering and thus a reducedmomentum resolution. For the phase I experi-ment, where muon rates rather than momentumresolution is limiting the sensitivity, a thicker tar-get could be envisaged.

Stopping 2 · 109 Hz muons in the target corres-ponds to about 1 mW of power. Compared withthe power dissipation of the sensor chips, this isnegligible and easily taken care of by the heliumcooling.

1Muons are generated with an energy spectrum model-ing the one observed in MEG.

39


9.2 Vertex distribution

The distances between tracks on the target canbe reconstructed already online and used by theevent filter farm to reject frames containing onlybackground, see section 14. The only physics pro-cess exhibiting three tracks from the same vertexis the radiative muon decay with an internal con-version at a rate of 3.5 · 10−5.

The simulated distribution of vertices (moreprecisely: intersections of simulated particles withthe target) is shown in Figures 9.2 and 9.3. Inthe longitudinal direction, the effect of the thickermaterial in the back part can be clearly discerned,whereas for the transverse view, the “shadows” ofthe target suspension are visible in the projectedbeam profile.

Figure 9.4 shows the shortest distance betweentwo vertices in a frame for 2 · 108 Hz muon stoprate. Less than 10% of the frames have tracksthat come within 1 mm of each other on the tar-get. Figure 9.5 shows the shortest distance withinwhich three tracks approach on the target sur-face; one of the tracks has to be assigned negativecharge, either because it is a true electron or a re-curling positron track. Figures 9.6 show the samedistributions for 2 · 109 Hz muon stop rate. Hereall frames have two tracks approaching to closerthan a millimeter, but a three track coincidencerequirement still has a considerable suppressionpower, which can surpass a factor of 10−3, if re-curlers can be identified with high efficiency (seealso chapter 14).

9.3 Alternative Designs

9.3.1 Material Alternatives

If the aluminium foil design proves unworkable ornot mechanically stable enough, it could be re-placed by an equivalent design in carbon fibre re-inforced plastic (CFRP), where the material thick-ness would be approximately double. 200 µm thinCFRP structures were built e.g. for the CMS pixeldetector upgrade [125].

Another material option would be the use of alow density foam-like material such as Rohacell,as used in the SINDRUM experiment [126].

Vertex z position [mm]-100-80 -60 -40 -20 0 20 40 60 80 100

Ve

rtic

es

0

500

1000

1500

2000

2500

310·

Figure 9.2: Vertex distribution along the beamdirection.

Vertex y position [mm]-10 -8 -6 -4 -2 0 4 8 10

Vert

ex x

positio

n [

mm

]

-10

-8

-6

-4

-2

0

2

4

6

8

10

0

200

400

600

800

1000

1200

1400

1600

1800

2 6

Figure 9.3: Vertex distribution transverse to thebeam direction.

40


Shortest Vertex-Vertex distance [mm]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.001

0.002

0.003

0.004

0.005

Vertex

pairs

per fram

e a

nd 0

.02 m

m

Figure 9.4: Shortest vertex-vertex distance insidea readout frame with 10 tracks on average (phaseIB). Note that every crossing of a simulated elec-tron/positron track is counted as a vertex. Thered histogram shows the contribution from in-ternal conversion decays.

Shortest e+e-e+ distance [mm]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.1

0.2

0.3

0.4

0.5

-310·

Vertex

trip

lets

per fram

e a

nd 0

.02 m

m

Figure 9.5: Shortest distance containing threevertices consistent with e+e−e+ inside a readoutframe with 10 tracks on average (phase IB).Note that every crossing of a simulated elec-tron/positron track is counted as a vertex; chargeassignments are made purely on the apparentcurvature, i.e. recurling positrons are counted aselectrons. The red histogram shows the contribu-tion from internal conversion decays.

Shortest Vertex-Vertex distance [mm]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Vertex

pairs

per fram

e a

nd 0

.02 m

m

0

0.01

0.02

0.03

0.04

0.05

0.06

Figure 9.6: Shortest vertex-vertex distance insidea readout frame with 100 tracks on average (phaseII). Note that every crossing of a simulated elec-tron/positron track is counted as a vertex. Thered histogram shows the contribution from in-ternal conversion decays.

Shortest e+e-e+ distance [mm]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Vertex

trip

lets

per fram

e a

nd 0

.02 m

m

Figure 9.7: Shortest distance containing threevertices consistent with e+e−e+ inside a readoutframe with 100 tracks on average (phase II).Note that every crossing of a simulated elec-tron/positron track is counted as a vertex; chargeassignments are made purely on the apparentcurvature, i.e. recurling positrons are counted aselectrons. The red histogram shows the contribu-tion from internal conversion decays.

41


9.3.2 Active target

We have also considered the use of our Kapton-sensor assemblies (see chapter 10) as an active tar-get. This would lead to a vertex separation abilityin the order of the pixel size (80 µm), as opposedto the ≈ 200 µm expected from track extrapola-tion. At an appropriate inclination angle, a wedgeof two chips with 6 × 2 cm2 active area and 50 µmthickness presents a comparable amount of mater-ial to the beam (however, the cabling and coolingrequired would add significant additional material

at least in the downstream direction). Such anarrangement would sacrifice φ-symmetry.

The hit rate expected in an active target exceeds3 GHz for high intensity running, correspondingto about 8 KHz per pixel, or 500 MHz per reticle,far beyond the 80 MHz expected in the innermostsensor layer. This in turn would necessitate thedevelopment of a completely new read-out blockfor the sensor chips. The gain in selectivity whengoing from ≈ 200 µm vertex resolution to 80 µmdoes not justify the cost and technical risks asso-ciated with the active target.

42

Chapter 10

The Mu3e Pixel Detector

The Mu3e pixel tracker is to be built from High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) thinned to 50 µm. Signal and powerlines are aluminum traces on a Kapton flex-print,which, together with a Kapton prism, also servesas a support structure. The detector should becooled with gaseous helium.

10.1 HV-Maps Sensor

We propose to use Monolithic Active Pixel Sensors(MAPS) as tracking detectors as they integ-rate sensor and readout functionalities in thesame device and thus greatly reduce the mater-ial budget. Classical concepts like hybrid designshave usually a higher material budget due to ad-ditional interconnects (bonds) and extra readoutchips, which compromise the track reconstructionperformance especially at low track momentum.

Figure 10.1: Sketch of the MAPS detector designfrom [127].

In the first MAPS designs ionization chargeswere collected mainly by diffusion with a tim-ing constant of several hundreds of nanoseconds.

MAPS designs with high bias voltages exceeding50 V, however overcome this problem by collectingcharges via drift and provide timing resolutions ofbetter than 10 ns.

We propose to use the High Voltage MAPSdesign with the amplifier electronics completelyimplemented inside the deep pixel N-well, whichwas first proposed in [127] and since successfullytested [128,129], see also section 10.4.

Figure 10.1 shows a sketch of a Monolithic PixelDetector. The readout circuitry allows an efficientzero suppression of pixel information and the im-plementation of timestamps to facilitate the as-signments of hits between different pixel layers.

For readout designs providing 50 − 100 ns tim-ing resolutions power consumptions of about150 mW/cm2 are expected [130].

Because of the small size of the active deple-tion zone, the detectors can be thinned down to50 µm or less. By thinning, the material budgetcan be significantly reduced and becomes, aver-aged over the tracking volume comparable to or-dinary gaseous detectors.

A further advantage is that HV-MAPS can beimplemented in a “cheap” commercial process.We use the AMS/IBM 180 nm HV-CMOS pro-cess [131], which was developed mainly for theautomotive industry, and thus offers long-termavailability as well as being specified for a verywide range of operating conditions. The processoffers a maximum reticle size of 2 × 2 cm2. Oneof the few disadvantages of the process is the factthat the first metalization layer is in copper, thusintroducing a small amount of medium Z mater-ial. There are however plans for replacing also

43


Small Sensor Large Sensor

Pixel Size [µm2] 80 × 80 80 × 80Sensor Size [cm2] 1.1 × 2 2 × 2Assembly 1 × 3 1 × 3Assembly size [cm2] 1.1 × 6 2 × 6Max. LVDS links 4 2Bandwidth [Gbit/s] 3.2 1.6

Table 10.1: Sensor specifications

that layer with an aluminium metalization in afuture version of the process.

Radiation-tolerance studies of the HV-MAPSsensors in 180 nm technology are ongoing also onother projects (e.g. ATLAS pixel R&D). Severaltest chips with similar pixel electronics as MUPIXhave been irradiated at PS (CERN) up to dosesbetween 80 and 430 MRad (the latest correspondsto a fluence of nearly 1 · 1016 neq/cm2). The res-ults are promising. Despite of the use of standardNMOS layouts, the chip irradiated to 80 MRadstill detects the particles radiated by a 90Sr source.The setup irradiated to 430 MRad is strongly ac-tivated, and no accurate detection of 90Sr sig-nals is possible. The chip was able to detectparticles from the beam up to 410 MRad dose.The main radiation effect is that the electronicssuffers from ionizing effects such that it is difficultto find a proper operation point for the pixel amp-lifier. As the Mu3e experiment is performed ata muon beam-line the requirements on radiationhardness are not comparable to those at hadroncolliders like the LHC. The radiation tests of theHV-MAPS sensors done so far all indicated thatthere will be no radiation damage even at highestmuon rates at phase II.

10.2 Sensor specification

We plan to use two types of sensors in the Mu3eexperiment, a smaller one for the inner layers anda larger one for the outer layers, see Table 10.1.The pixel size is 80 × 80 µm2, much smaller thanthe multiple scattering contribution.

The wafers are to be thinned to 50 µm. If theyields permit it, we will cut strips of three sub-sequent sensors from the wafers and mount themin one piece.

The sensor output is zero suppressed and con-sist of time-stamps and addresses of hit pixels,

serialized on a 800 Mbit/s low voltage digital sig-naling (LVDS) link. The sensor is configured via aJTAG interface [132]. Including supply voltages,we expect about 30 pads (and thus bond wires) toconnect the chip to the Kapton flex-print.

10.3 Path towards the Full Sensor

10.3.1 The MUPIX Prototypes

First purpose-built sensor prototypes (the MUPIXseries of chips) became available in 2011.

MUPIX1 and 2

The MUPIX 1 and 2 are small demonstration pro-totypes with a matrix of 42 × 36 pixels of 30 ×39 µm2 size for an active area of approximately1.8 mm2, see Figures 10.2 and 10.4. Each pixelconsists of the sensor diode, a charge-sensitiveamplifier and a source follower to drive the signalto the chip periphery. In addition there is a capa-city allowing to inject test charges. On the peri-phery, a comparator turns the analog signal intoa digital time-over-threshold (ToT) signal. Thethreshold of the comparators is set globally forthe chip and adjusted pixel-per-pixel with a 4-bittune digital to analog converter (DAC). See Fig-ure 10.3 for an overview of the pixel electronics.In the test chips, the comparator output of anindividual pixel can be observed via a dedicatedoutput line. Alternatively, the whole chip can beread out via a shift register, where all the avail-able information is whether a particular pixel sawa signal during an active gate.

The MUPIX 1 chip had an issue with feedbackin the comparator that occasionally led to doublepulses. This issue has been fixed in MUPIX 2,which in addition contains temperature sensors.

MUPIX3

In August 2012, we submitted the MUPIX 3 chip,a major step towards the final sensor. The newchip has 40 × 32 pixels of 92 × 80 µm2 size foran active area of approximately 9.4 mm2, see Fig-ure 10.5. It implements the full digital columnlogic, allowing for address generation and serialreadout of zero-suppressed data. In addition,MUPIX3 has faster signal shaping.

The main differences with the final sensor arethe lack of a high-speed LVDS output, buffers in

44


Figure 10.2: Design view of the MUPIX2 chip (ac-tual size about 1.8 by 2.5 mm).

Source Follower

To Digital Processing Unit

Figure 10.3: Schematic of the pixel cell analogelectronics in the MUPIX chips. nw stands forn-well.

Figure 10.4: MUPIX2 sensor on ceramic carrierwith one Euro-cent for scale comparison.

Figure 10.5: Design view of the MUPIX3 chip (ac-tual size about 4 by 5 mm).

the columns and the chip-wide hit collection logic.For this prototype, the corresponding logic will beemulated off-chip in an FPGA. Also several con-trol voltages which should be generated on-chip inthe final version are currently produced on a testprinted circuit board (PCB) in order to allow foreasier debugging.

We have just received the first MUPIX 3samples. First test results will become availableearly 2013.

10.3.2 Plans for 2013

As soon as the first results from the MUPIX 3sensor are available, we will prepare anothermulti-project-wafer (MPW) run, implementingthe remaining digital logic and addressing poten-tial issues discovered with MUPIX 3. This shouldclear the path for an engineering run in the secondhalf of 2013, opening up the possibility to build afull scale tracker prototype.

45


10.4 Characterization of the Proto-

types

We have studied the properties of the MUPIX 1and 2 prototypes using injection pulses, LEDs,laser diodes, X-rays, radioactive sources and testbeam measurements. In the following, we will out-line the core results; details of the findings can befound in a master [133] and a bachelor thesis [134].

The test setup was based on a test board hous-ing the chip itself and a logic interface card. Thechip test board has voltage regulators for the sup-ply voltages, digital to analog converters for thethreshold and injection pulse height and a flat rib-bon connector to the logic interface card. This in-terface card uses a FPGA both to program andreadout the MUPIX chip and to communicatewith a PC via USB. These two boards togetherwith a C++ control software have been used forall tests described here.

10.4.1 Signal to Noise Ratio

Injection pulses can simulate the charge depos-ition of ionizing particles. A scan of the injectionpulse height at constant threshold would delivera step function if no noise were present. Due tothe additional noise on top of the injection pulsethe step function is transformed to an error func-tion with a finite slope. In turn the width of thestep function can be used to determine the noiseas a function of the applied threshold. A 55Fesource has been used as reference signal for thedetermination of the signal to noise ratio (SNR).The injection pulse height corresponding to the55Fe signal is found by matching the time overthreshold of both signals at a given threshold. Forthe MUPIX 2 chip the signal to noise ratio asa function of threshold ranges between 21.5 and35.7, see Figure 10.6. Any signal to noise ratio >9is considered good.

10.4.2 Pixel to Pixel Uniformity

Using a similar method as for the measurement ofthe signal to noise ratio, the pixel to pixel uni-formity can be determined and optimized. Ata constant injection pulse height a scan of thethreshold setting for the entire pixel matrix is car-ried out. For each pixel the error function fit isperformed and the 50 % value of the error func-tion rising edge plotted, see Figure 10.7a). As can

Threshold [V]0.82 0.84 0.86 0.88 0.9 0.92

SN

R

0

5

10

15

20

25

30

35

40

Figure 10.6: Signal to noise rate for the MUPIX 2chip. The signal size is taken from measurementswith a 55Fe source, whilst the noise is measuredin a injection pulse scan, see [133] for details.

be seen in Figure 10.7c) the distribution of thethreshold values for the pixels of the same chipis quite broad. In order to compensate for theseinequalities, a threshold offset, the so called tuneDAC (TDAC) value can be set for each pixel. Thebest TDAC values for the pixels are found by run-ning an automated procedure, see [133]. Figure10.7b) and d) show that the threshold spread (re-flecting the response uniformity) after tuning thethreshold offsets has decreased by almost an orderof magnitude from 19.6 mV to 2.3 mV RMS.

10.4.3 Pixel Response Time

The timing characteristics of the MUPIX chip isvery important because of the requirement to runat high muon decay rates. A fast response of theMUPIX chip leads to precise timing of hits andhelps suppressing combinatorial background. Inthe inner detector layers the double pulse resolu-tion should be good as the hit rate is up to 2 kHzfor each pixel.

Timing studies have been carried out using aLED driven by a pulse generator to stimulate thesensor. The discriminator output of a single pixelis then compared to the second output of thepulse generator on an oscilloscope. In this con-figuration it is possible to measure the latencybetween generator and pixel output and the timeover threshold (ToT) of the pixel. By plottinglatency and ToT for many threshold values oneobtains the pulse shape, see Figure 10.8. Themeasured pulse shape reflects the RC-CR shaping

46


Column0 5 10 15 20 25 30 35 40

Ro

w

0

5

10

15

20

25

30

35T

hre

sho

ld [

V]

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

(a) Before tuning

Column0 5 10 15 20 25 30 35 40

Ro

w

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5

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20

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35

Th

resh

old

[V

]

0.96

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1.1

(b) After tuning

Threshold [V]0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Num

ber

of

Pix

els

1

10

210

(c) Before tuning

Threshold [V]0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Num

ber

of

Pix

els

1

10

210

(d) After tuning

Figure 10.7: Uniformity of the pixel response before and after tuning of the pixel DAC values, from [133].

47


Time [µs]0 1 2 3 4 5 6 7

Thre

shold

[V

]

0.85

0.9

0.95

1

1.05

Figure 10.8: Measured pulse shape of a MUPIXpixel in response to an LED pulse, fitted with theexpectation from RC − CR shaping, from [133].

Delay [µs]1.5 2 2.5 3 3.5 4 4.5

Rat

io [

%]

0

20

40

60

80

100

Data

ErrFct-Fit

1% level

Figure 10.9: Double pulse resolution of theMUPIX2 chip, from [133].

characteristic of the pixel electronics. The chargecollection process in the depletion zone is muchfaster and has little influence on the measured tim-ing.

By generating double pulses and dividing thenumber of unresolved pulses at the pixel outputby the number of all pulses, the double pulse res-olution can be determined. Figure 10.9 shows thisratio as a function of pulse to pulse delay. An er-ror function has been fitted and the point of 1 %un-resolved pulses gives a double pulse resolutionof 2.7 µs consistent with the expectation from thechosen shaper characteristics.

ToT [µs]0 1 2 3 4 5

-410

-310

-210

-110

1

Figure 10.10: Time-over-threshold (correspondingto energy) spectrum of a 55Fe radioactive source,from [133].

10.4.4 Measurements with RadioactiveSources

Radioactive sources allow to test the MUPIXchips with real particles. For a 55Fe source thetime over threshold (ToT) distribution, which isan measure for the energy distribution, is shownin Figure 10.10. X-ray fluorescence in the rangeof 4 to 18 keV has been used to derive a relativeenergy resolution of 10 to 20 %.

The 55Fe peak in the ToT spectrum has beenused to study the influence high voltage (HV) andtemperature on the pixel signal. Figure 10.11shows the 55Fe peak as a function of the HV,revealing first a steep rise as the depletion zonegrows. Between 20 and 60 V, the ToT stays al-most constant. At even higher voltages the elec-tric field in the depletion zone becomes strongenough for the creation of secondary electron-holepairs, which results in a signal amplification. Thetemperature dependence of the pixel sensor is im-portant, because in the later experiment the differ-ent parts of the detector will operate at differenttemperatures varying by 30-40 C. In Figure 10.12the 55Fe peak of the ToT spectrum is plotted as afunction of temperature between 20 to 60 C. Ascan be seen the ToT goes down from 1.6 to below1 µs, with a slope of 16.3 ns/C. Measurementswith test pulse injection and simulation studiesconfirm that the observed temperature depend-ence is a feature of the charge sensitive amplifierof the pixel analog stage.

48


High Voltage [V]0 10 20 30 40 50 60 70 80 90

Posi

tion o

f F

e P

eak [

µs]

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Figure 10.11: Position of the 55Fe peak in depend-ence of the applied high voltage, from [133].

Temperature [°C]30 40 50 60 70 80

Posi

tion o

f F

e P

eak [

µs]

0

0.5

1

1.5

2

2.5

3

3.5

4

Figure 10.12: Temperature dependence of the po-sition of the 55Fe peak, from [133].

10.4.5 Testbeam results

In August 2012 the MUPIX2 chip was tested atthe CERN SPS. The beam from the SPS was a170 GeV pion beam, chosen for little multiple scat-tering effects due to the device under test (DUT).In two separate data taking periods the MUPIX2was mounted inside the TimePix telescope [135].This silicon pixel telescope has four layers beforeand four layers after the DUT, providing very pre-cise pointing resolution of 5 µm. The MUPIX2chip was tested facing the beam and under anangle of 45. For both beam periods a thresholdscan was performed in order to derive the effi-ciency as a function of threshold, but no thresholdcalibration to equalize the gain of the pixels wasperformed. Figure 10.13 shows the resolution inx and y direction of the MUPIX2 chip facing the

Figure 10.13: Resolution of the MUPIX 2 chipmeasured in a testbeam with 170 GeV pions andthe TIMEPIX telescope. The measured resolu-tions correspond very well to the expectation fromthe 5 µm resolution of the telescope and the pixelpitch in x and y direction, respectively.

Figure 10.14: Tool for layer 3 segment assembly.

beam and tested at three different threshold val-ues. The measured resolution of 11.2 µm in x and15.4 µm in y corresponds to the expected resolu-tion given the telescope resolution and the pixelsize. Further results are still subject to studiesand will follow soon.

10.5 Mechanics

The pixel detector mechanics has been optimizedfor very low material budget in the active detectorregion. Additional requirements are mechanicalstability, resistance to temperatures over a widerange and a modular design for ease of assemblyand repair. It is proposed to build the frame forthe silicon pixel detector from thin Kapton foil.The sensors are glued and bonded on a flex-printand then mounted onto the Kapton frame.

49


Figure 10.15: Tool for layer 3 segment assembly.

Figure 10.16: Mechanics of the central pixel de-tector

Figure 10.17: Segmentation of the central outerlayers.

Figure 10.18: Mounting tool for the central pixeldetector.

The Kapton foil used for the mechanical frameconstruction is 25 µm thin. It gains in mechan-ical stability as it is folded around a prism-shapedtemplate and glued to plastic end-pieces. For thisprocess tools have been built, which support thedetector modules until they are ready for full sta-tion assembly, see Figures 10.14 and 10.15. In aseparate tool the 50 µm thin pixel chips are gluedon the single layer Kapton flex-print. Alignementgroves secure the correct position of the chips. Inthe next step the chips are wire bonded to theflex print. With a vacuum lift tool the flex-printsare then positioned and glued to the mechanicalframes. The radiation length of a pixel detectorlayer is summarized in Table 10.2.

The pixel detector is build from layers of fourdifferent sizes and prism shapes, see Figure 10.16.As the digital readout circuits of the pixel chipscreate an approximately 0.5 mm wide dead area,there is a 1 mm overlap to the adjacent sensor.The inner double layers have 12 cm active length.Layer 1 has 12 and layer 2 18 sides of 1 cmwidth. Each inner layer is assembled from twohalf-modules. As a consequence the plastic end-pieces are half moon shaped. When all fourhalf modules of the inner detector layers are pro-duced and tested they are mounted to two thinrim wheels. A mechanical prototype for the in-ner double layer has been constructed from 25 µmKapton foil both for the frame and the flex-printlayer, while the pixel chips have been simulatedwith 100 µm thick glass plates. Glass of 100 µmthickness is of comparable flexibility as thinnedsilicon, which is shown in Figure 10.19. The res-ulting mechanical unit is surprisingly sturdy andfully self supporting, as can be seen in Figure

50


Component thickness X/X0

[µm] [%]

Kapton frame 25 0.018Kapton flex-print 25 0.018Aluminum traces 15/2 0.008(50 % coverage)HV-MAPS 50 0.053Adhesive 10 0.003

Full detector layer 125 0.100

Table 10.2: The pixel detector layer radiationlength is dominated by the HV-MAPS chips.

10.20. Layer 3 and layer 4 have a three times lar-ger active length of 36 cm. The sides of these outerlayers are 19 mm wide. The layers 3 and 4 have24 and 28 sides. An outer double layer modulecombines four sides, so layer 3 consists of 6 andlayer 4 consists of 7 modules, see Figure 10.17.The station assembly is done in a special mount-ing frame, combining the inner two layers withthe modules of the outer two layers on large rimwheels (Figure 10.18). Re-curl stations will be as-sembled accordingly.

10.6 Cooling

The cooling system for the pixel detector must becapable of keeping the temperatures at a reason-able level (≤ 70 C) and should at the same timeadd very little extra material to the active volumeof the detector. Cooling with gaseous helium hasbeen chosen as it appears to offer a reasonablecompromise between cooling potential and radi-ation length.

Given its size, the heat load introduced by thepixel detector is considerable. Table 10.3 de-tails the contributions of the different parts ofthe pixel detector assuming a realistic heat loadof 150 mW/cm2. It is worth mentioning thatthe heat load is strongly dependent on the clockspeed at which the pixel chips are running. Pixelchips with very low occupancy, for example thoseinstalled in the recurl stations, could optionallybe operated at half the clock speed which wouldlargely reduce the total thermal power of the pixeldetector.

In order to keep the temperature of the coolantequally low in all parts of the detector, it is fore-

Detector Part size [cm2] power [W]

layer 1 158.4 23layer 2 237.6 35vertex layers (1+2) 396 59layer 3 1728 259layer 4 2016 302outer layers (3+4) 3744 561central detector (1-4) 4140 621detector with2 recurl stations 11628 1744full detector 19116 2867

Table 10.3: Pixel detector heat load for150 mW/cm2

seen to place nozzles between the support struc-tures pointing at different parts of the sensor lay-ers.

In order to study the potential of gaseous he-lium cooling a bachelor thesis has been carriedout [136]. In this thesis a thin sandwich of alu-minum foil, Kapton and silicon was heated induct-ively and cooled with a helium flow. For the 8.5 cmlong sample heated with 100 mW/cm2 a flow of0.4 m/s was necessary to maintain a temperaturedifference between helium and sensor of 32 K. Fur-ther studies using a full scale central detector pro-totype in a wind tunnel are on the way. This fullscale prototype will be assembled from aluminizedKapton foil such that Ohmic heating can be ap-plied. It is planned to run the upcoming tests withthe helium heat exchanger acquired for phase I ofthe experiment.

10.7 Alternative Technologies

Since the Mu3e pixel detector plays the key role inthe experiment, it is important to carefully com-pare the chosen HV-MAPS technology with al-ternatives. To do so one has to have the detectorrequirements in mind, see chapter 5. The goal of abranching ratio sensitivity of 10−16 leads to a highmuon decay rate on target of 2 · 109 Hz. In orderto suppress combinatorial background a very goodvertex resolution of O(200 µm) is needed. Thesuppression of the background from the conver-sion decay µ → eeeνν requires very precise mo-mentum reconstruction of better than 0.5 MeV,for the 10−16 branching ratio sensitivity. The

51


Figure 10.19: A 50 µm thin silicon wafer.

Figure 10.20: Mechanical prototype of the inner pixel layers. Thin glass plates replace the silicon chips.

52


momentum resolution for the low energetic decayproducts of 10 MeV to 53 MeV will be governed bythe multiple scattering in the detector. Only con-cepts with extremely low radiation length of <1 %in total can achieve this.

In the following different technology optionsfor the Mu3e tracking detector are compared.The result of this comparison is summarized intable 10.4.

10.7.1 Time-Projection Chamber

Time projection chambers are a very attractiveconcept for tracking detectors with good spacialresolution and very low radiation length. The ex-ample of the ALICE TPC [137] has demonstratedthat very high track densities can be handledwith such a detector. Over the last two dec-ades many studies for TPCs with very low radi-ation length, i.e. 0.12 % for a proposed chamber atSLAC [138], have been carried out. The drift timeof an electron in a possible TPC for the Mu3e ex-periment with 2 m total length would be in theorder of 50 µs, using the proposed gas mixtureof Helium:CO2:Isobutane (83:10:7%). This timeof 50 µs at 2 · 109 Hz decay rate means that theDAQ and event filter farm would have to handleframes containing >105 muon decays, which is notrealistic. Another problem would be strong spacecharge effects due to continuous very high trackdensity, see [139]. These two aspects rule out theusage of a TPC in the phase IB and phase II ofMu3e, while it would be possible to use a TPC inphase IA.

10.7.2 Other Pixel Technologies

The usage of pixel detectors in particle and heavy-ion physics has recently lead to a variety of thindetectors capable of dealing with high particlefluxes. It is worth to discuss the solutions de-veloped for the upgrades of the STAR, BELLEand LHCb vertex detectors.

The STAR upgrade vertex detector [140]is based on Monolithic Active Pixel Sensors(MAPS), more precisely the MIMOSA 28 sensor[141]. The vertex detector under construction islocated around the interaction point at r=2.5 cm,8 cm and has an intrinsic hit resolution of <6 µm.An ultralight carbon fibre support structure hasbeen developed with a thickness of 200 µm. Theradiation length is X/X0=0.079 % per layer in theactive region. The power dissipation is about

170 mW/cm2 and forced air cooling at 10 m/s isused [142]. The charge collection for the MIMOSAchips is based on electron diffusion, resulting incharge collection times of 50 ns. This has to becompared to the charge collection times of driftbased silicon detectors like silicon strip and hy-brid silicon pixel detectors of a few ns. The signalintegration of the MIMOSA 28 chip is 185.6 µs.This long integration time corresponding to >105

decay events rules out the usage of the MAPS de-veloped for STAR vertex upgrade in Mu3e,

Belle2 is building a lightweight silicon vertextracker based on DEPFET pixel sensors [43]. TheBelle2 silicon vertex detector has two layers atr=1.4 cm, 2.2 cm. The monolithic sensors areonly 75 µm thick and self supporting, resultingin a radiation length of X/X0=0.18 % per layer[143]. The cooling system uses liquid CO2 for thereadout electronics and cold dry air with forcedconvection for the sensors. The sensor chip isequipped with an integrated read out amplifica-tion, the charge is then accumulated internally.The readout is enabled externally and done in arow wise rolling shutter mode. The readout timefor the entire chip is 20 µs. As for the MIMOSA 28sensor the relatively long readout time makes theBelle2 DEPFET sensor unsuitable for the Mu3edetector. On top of this the Belle2 DEPFETsensor produces analog output signals and re-quires further electronics for analog to digital con-version, baseline subtraction, discrimination andzero-suppression.

The proposed pixel detector for the LHCb ver-tex upgrade belongs to the TIMEPIX family ofchips. The main goal of the LHCb upgrade is tomove from a 1 MHz readout to a 40 MHz readoutin order to make a track based L0-trigger possible.The power consumption per chip is 1.5 W/cm2

[144], which is quite high. The sensor thickness is150 µm to 200 µm. The LHCb Velo upgrade pixelsensor is a hybrid design, so in addition to thesensor there is also the readout chip thickness, thesolder bump bonds, aluminum traces and coolingelements summing up to X/X0=0.73 % per layer.In LHCb the vertex detector is inside a vacuumtank around the interaction point, so the cool-ing scheme relies on a high thermally conductivespine (diamond) in combination with a liquid CO2

cooling outside the active area. Alternative cool-ing studies look at micro-channel cooling whichwould extend the CO2 cooling to the pixel chipsin the active area. The pixel sensor is designed to

53


Mu3e STAR BELLE LHCbParameter required HV-MAPS He TPC MIMOSA28 DEPFET VeloPix

sensor thickness X/X0 [%] ≤0.1 0.075 - 0.079 0.18 0.73readout cycle [µs] ≤ 0.1 0.05 50 185.6 20 0.025power [mW/cm2] ≤ 200 150 - 170 100 1500

Table 10.4: Alternative technology comparison, only the crucial parameters are listed.

have less than 25 ns time-walk at 1000 electrons.The output bandwidth is > 12 Gbit/s with on-chipzero suppression. The readout is hit driven andasynchronous. While the readout speed would beideal for the Mu3e detector, the radiation lengthper layer of X/X0=0.73 % is too high.

10.7.3 Conclusion

In the field of tracking detectors with good res-olution, low radiation length and high rate cap-abilities there has been a very strong progress inthe recent years, see Table 10.4. Time projectionchambers with helium gas mixtures would provideexcellent momentum resolution. Because of thevery long drift times in a large TPC and the con-stantly high muon decay rates, it is not possible todo online track reconstruction in the event filter

farm for decay rates exceeding 1 · 107 Hz, whichcorresponds to phase IA of the Mu3e running. Asa change of technology between phases IA and IBis not desirable, the TPC option can only be con-sidered as a back-up solution.

The above discussed pixel alternatives can begrouped in two categories. The systems basedon the MIMOSA chip for the STAR upgrade andthe DEPFET chip for Belle 2 have little radiationlength of X/X0=0.079 % and 0.18 % per layer, buthave long readout cycles. On the other hand theVeloPix based tracker for the LHCb upgrade canbe read out at 40 MHz, but has a relatively largeradiation length of X/X0=0.73 % per layer. Inall three cases further R&D would be required totransform the existing designs into one fulfillingthe requirements of all phases of the Mu3e exper-iment.

54

Chapter 11

The Mu3e Fibre Detector

11.1 The time of flight detector

Target

Inner pixel layers

Scintillating !bres

Outer pixel layers

Figure 11.1: Schematic side view (left) and crosssection (right) of the detector components. TheSci-Fi system is highlighted in blue.

A cylindrical time of flight (ToF) detector com-plements the central silicon tracking system. Itconsists of a scintillating fibre (Sci-Fi) hodoscopewith a radius of 6 cm and a length of 36 cm. Theexpected time resolution is of several 100 ps anda detection efficiency close to 100 %. The mainpurpose of the ToF system is to measure very pre-cisely the arrival time of particles in order to allowfor the matching with hits detected in the silicondetectors. This will help to reject pile-up events(accidental backgrounds) and allow for a charge(direction of propagation) measurement for recurl-ing tracks. The ToF system will operate at veryhigh particle rates up to several MHz per channel.

A detailed R&D program is ongoing to provethe feasibility of the Sci-Fi detector and to helpoptimizing the design of the Sci-Fi detector. TheR&D activity covers all the aspects of the ToF

detector development: scintillating fibres, SiPMs,amplifiers, and readout electronics. The chal-lenging aspects of the ToF system are (i) thehigh rates per Sci-Fi readout channel and (ii)the large data flow generated by the readout di-gitizing electronics, which has to be handled inreal time. Time resolutions of about 200 to300 ps have been already achieved with Sci-Fihodoscopes with single-ended readout using multi-anode PMTs [145]. We aim at a similar time res-olution.

In the current design, the scintillating fibre de-tector is composed of 24 Sci-Fi ribbons, each 36 cmlong and 16 mm wide, as illustrated in Figure 11.2.The ribbons will be supported by a carbon fibremechanical structure. The use of 250 µm dia-meter multi-cladding scintillating fibres producedby Kuraray is envisaged. Three to five Sci-Filayers (Figure 11.2 right) are staggered such asto minimize empty spaces between fibres. Fig-ure 11.3 shows a Sci-Fi ribbon and its cross sec-tion. In the figure the uniform staggering of theSci-Fi layers can be seen. The overall thickness ofthe Sci-Fi arrays varies depending on the numberof layers between 0.6 to 1 mm. This thickness hasto be kept as low as possible, to reduce the mul-tiple scattering to a minimum compatible with therequired performance (i.e. time resolution and ef-ficiency). The empty space between adjacent rib-bons will be minimized in order to guarantee con-tinuous coverage.

The scintillating light produced in the fibres willbe detected with SiPM arrays at both fibre ends.The choice of SiPMs as a photo-detection device isbased on the fact that they are very compact ob-

55


Figure 11.2: Left: Overall view of the Sci-Fi barrel ToF detector. The diameter of the detector is about12 cm, the length about 36 cm. Middle: Detail showing the SiPM ceramic supports and the Sci-Fi arrays.Right: Details of the Sci-Fi ribbons. In this figure, the ribbons consist of five staggered Sci-Fi layers.

Figure 11.3: Photos of a Sci-Fi ribbon (left) and of its cross section (right). The uniform staggering of4 Sci-Fi layers is clearly visible.

jects that can be operated in high magnetic fieldswith high gain (∼ 106) and at high counting rates.

Two different readout schemes for the fibres arebeing considered and investigated: 1) fibres aregrouped in vertical columns (this is implementedby the structure of the readout photo-device), 2)each fibre is read out individually. In the firstdesign we envisage to use the 32 channel SiPM ar-rays with 50 × 50 µm2 pixels available from Hama-matsu [146, 147]. The active size of the sensor is8 × 1.1 mm2 with a total surface of 9 mm2. Thepixels are arranged in columns, corresponding toan effective pitch of 250 µm. Two such SiPMsensors will be assembled side by side with al-most no dead region, giving a 16 mm wide photo-sensitive region with 64 readout channels, andmatching precisely the width of the Sci-Fi ribbons.The photo-detectors will be directly coupled to theSci-Fi arrays to maximize the light collection effi-ciency, and consequently the timing performance.In total 96 SiPM arrays with 32 channels each willbe required to readout the Sci-Fi tracker at each

end, for a total of 2 × 24 × 64 (∼ 3000) readoutchannels.

A detailed understanding of the expected occu-pancies in the the Sci-Fi detector is required. Therates depend also on the background in the de-tector generated by secondary interactions in thematerials of the different components. A particlecrossing the Sci-Fi ribbons at 90, will excite oneor two adjacent Sci-Fi columns, as sketched in Fig-ure 11.4. A particle crossing the same Sci-Fi rib-bon, for example at 45, will excite 4 to 5 adja-cent Sci-Fi columns for a 5 layer ribbon and 2 to3 for a 3 layer ribbon, thus increasing significantlythe overall occupancy of the detector. At an ex-pected rate of 1.5 · 109 muon decays per secondusing 1500 Sci-Fi channels, the estimated rate inthe Sci-Fi system is 5 MHz on average. At thesame time the signal will be spread out over sev-eral SiPM channels. A well designed clusteringalgorithm will be required to reconstruct the tim-ing and position of the crossing particle.

The lowest possible detector readout occupancycan be achieved by reading out each fibre indi-

56


vidually. In absence of dark current noise andbackground, the occupancy is given by the rateof detected electrons from muon decays and is ex-pected to be 1 MHz per fibre. When reading outeach multi-cladding fibre individually, one has totake into account that the scintillating light travelspreferentially in the cladding of the fibre and exitsthe fibre in a cone with an aperture of about 45.In order to collect all the scintillating light exit-ing the fibre, and thus ensure high detection effi-ciency, the photo-detector has to be wider then thefibre diameter, at least 100 µm around the fibre.This compensates also the misalignment, of the or-der of few tens of microns, between the fibres andthe SiPMs. In order to avoid the light from onefibre to spill over to a neighboring photo-detectorchannel (optical cross-talk) the fibres and photo-detectors have to be separated by 500 µm center-to-center. To summarize, the estimated, optimalsize of the photo-detector for reading out each250 µm fibre individually is 400 × 400 µm2 (for asquare device), and a center-to-center separationof 500 µm.

A transition region between the highly compactSci-Fi ribbons and the photo-detectors of about5 cm will be required to fan-out the Sci-Fis to thedesired center-to-center separation of 500 µm be-fore coupling the fibres to the SiPMs. To assurethe precise alignment, the fibres will be glued insockets with a precision of 10 µm. The SiPMs willbe coupled to the Sci-Fis using the same sockets.Reading out each fibre individually will require atotal of about 9000 readout channels.

In case the SiPMs could not be coupled dir-ectly to the Sci-Fis (because of mechanical con-straints inside the limited space), optical fibrescoupled to the Sci-Fis will be used to transmit thescintillating light outside of the solenoid, wherethey will be coupled to the same type of SiPM ar-rays, however with some loss of light. In this casethe use of multi-anode PMTs or multi-channelplate PMTs could be also envisaged as alternat-ive photo-detector device to the SiPMs for thereadout of the Sci-Fi ribbons.

Different manufacturers are also being investig-ated. The reported photo-detection efficiency ofthe Hamamatsu SiPMs is not that high (PDE ∼25 %). Since the time resolution depends on thenumber of detected scintillating photons (στ ∼1/

√nph) in order to obtain the best timing per-

formances we need to maximize the PDE of theSiPM arrays. Discussions with Hamamatsu to ex-

Figure 11.4: Sci-Fi occupancy vs. particle crossingangle and position. Dark fibres indicate higherenergy deposit.

plore various possibilities to increase the PDE areongoing. We will also discuss with other compan-ies capable of producing such devices (we alreadycontacted FBK in Italy and Ketek in Germany).Very likely it will be required to design SiPMsensors matching precisely the requirements of theSci-Fi detector rather than using commerciallyavailable SiPMs.

Performance studies of Sci-Fi ribbons coupledto SiPM arrays will be carried out in test beamsat PSI. The test beam activities will include thestudy of the time resolution, rate capabilities, de-tection efficiency, tracking resolution, and uni-formity of the detector. Different readout elec-tronics will be also tested.

11.2 Readout of photon detectors

For the readout of the SiPMs different options arebeing investigated. Details are given in chapter13.

One possibility is to use the well-establishedwaveform digitizing technology based on the DRSswitched capacitor array chip developed at PSI.The advantage of this technology compared totraditional constant fraction discriminators andTDCs is that pile-up can be effectively recog-nized and corrected for. Due to the bulkiness ofthis readout electronics, the digitizing electronicscannot be located in the proximity of the Sci-Fidetector. To transmit the electrical pulses fromthe SiPMs to the digitizing electronics two op-tions are being considered. In a first version thesignals are transmitted without amplification onshielded low attenuation coaxial cables. Giventhe low amplitude of the pulses (1.5-2 mV perphoto-electron) and potentially high noise fromthe digital readout electronics, the amplificationof SiPM signals might be required. In this secondversion the pulses are first amplified about a factor

57


x hitpos [mm]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

y hi

tpos

[mm

]

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-0.3

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Figure 11.5: Simulated photon output integratedover 1000 positron crossing events for a specificfibre geometry (top) with the corresponding timedistribution of the SiPM response using a constantfraction discriminator algorithm with a FWHM ofabout 300 ps (bottom).

of ten and then transmitted. Hybrid amplifiercircuits will be installed on the other side of theSiPM mountings. We already developed fast amp-lifiers using transistors (rise time ∼ 1 ns, decaytime ∼ 10 ns) matching the input characteristicsof SiPMs for optimal time performance and highrates.

A second possibility is to use the STiC chip,which includes a fast discriminator and a TDCdigitizing the time information. The advantage ofthis solution is the compactness of the chip thatcould be installed very close to the SiPMs, withno need to amplify and to transmit analog signals

outside of the solenoid. A third option could beoffered by time to digital converters implementedin FPGAs.

11.3 GEANT simulations

To optimize the overall design of the detector andof the Sci-Fi sub-system in particular, extensivesimulation studies are being carried out. We areexploring the propagation of scintillating light inthe fibres in a dedicated simulation that allowsto compare the optical properties for any possiblefibre and ribbon geometry. Meanwhile a completeset of simulation tools is available which allows aprofound analysis of the different possible layoutsof the Sci-Fi system.

Ongoing simulation studies will help us to op-timize and work out the details of the final Sci-FiToF design. Given that a crucial requirement ofthe experiment is to minimize all involved mater-ials also a layer of reflecting paint or glue will addadditional non active material to the detector andthus increase the overall material budget seen bythe particles crossing the Sci-Fi ribbons, resultingin a deterioration of the overall momentum res-olution of the tracking system. This and similareffects can now be studied easily with the availabletools.

In combination with a simulation of the SiPMresponse [148], we are now able to estimatewhether the aimed time resolution of a few hun-dred picoseconds is feasible with the fibre geo-metry and the SiPMs under investigation. Firststudies show that the resolution can be achievedwith the baseline design (Figure 11.5). Furtherfibre geometries and readout combinations arecurrently being evaluated. In addition to the sim-ulation test setups are being developed consist-ing of a complete ribbon with the SiPM detect-ors mounted on both ends to verify the simulationresults and to get the prove whether the desiredgeometry can be constructed with reasonable ef-fort. Furthermore the test stand will be used toevaluate readout electronics.

An additional source of concern is the cross talkand after pulsing observed in most APDs operatedin Geiger mode. Both effects will lead to an in-crease of the occupancy of our electronics channelsand thus have to be minimized. Since the Sci-Firibbons are read-out on both ends, this uncorrel-ated source of noise, in principle, can be rejected.

58

Chapter 12

The Mu3e Tile Detector

Figure 12.1: Drawing of a tile detector modulewith 48 × 48 tiles.

The second component of the Time-of-Flighthodoscope is a detector consisting of scintillatingtiles which are, as in the case of the Sci-Fi tracker,read out by SiPMs. The tile detector is located inthe recurl station on the inside of the recurl pixellayer (see Figure 6.5). The detector aims at a timeresolution of below 100 ps and an efficiency closeto 100% in order to effectively identify a coincid-ent signal from three electrons and suppress com-binatoric background. The main challenge of thedetector design is to achieve these requirementsunder the high hit rate which is expected, espe-cially in phase II.

12.1 Detector Design

The detector is divided into four modules (one foreach recurl station) with a length of 36 cm and

diameter of ≈ 12 cm. Each module is segmentedinto small tiles with a size of O(1 cm3), which areindividually wrapped in reflective foil in order toincrease the light yield.

In the current design, each module consists of48 rings with a thickness of 5 mm, and each ringconsists of 48 tiles (see Figure 12.1). This resultsin a total number of 2304 tiles per station, anda tile geometry of roughly 7.5 × 7.5 × 5 mm. Forthe outer two recurl stations, the number of tilesmight be decreased to 36×36 due to the lower hitrate (see Figure 12.2), in order to reduce the costs.This detector geometry is the result of extensivesimulation studies which will be continued in orderto further optimize the detector performance.

The tiles are made of plastic scintillator mater-ial which provides a fast light response. The mainrequirements for the scintillator are a high lightyield, fast rise and decay time and a scintillationspectrum which approximately matches the spec-tral sensitivity of the SiPM. Different scintillatorshave been compared using a Geant4 simulationin combination with a simulation of the SiPM re-sponse. The best suited scintillator was found tobe BC420 from Bicron. However, the differencesbetween the individual scintillating materials werefound to be small, and thus also more inexpensivealternatives are feasible.

The scintillation light of each tile is read out bya SiPM which is directly attached on the inside ofthe tile. SiPMs are well suited for this applicationdue to the compact size, insensitivity to magneticfields, high photon detection efficiency (PDE) andexcellent timing properties. The most importantSiPM characteristics for this application are a high

59


z position [mm]-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Hit

rate

/ til

e [M

Hz]

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Figure 12.2: Hit rate per tile for phase II. The ratefor phase I is a factor 10 to 20 smaller.

PDE and gain in order to obtain a large signaland therefore a good time resolution. Further-more, a small signal decay time is desired in orderto reduce signal pile up and thus increasing thesignal efficiency. The S10362-33-050 MPPC fromHamamatsu with an active area of 3 × 3 mm2 and3600 pixels is a suitable sensor for this applica-tion. A possible alternative sensor is the PM3350from Ketek which offers a larger PDE and gaincompared to the Hamamatsu device, but has alonger decay time. A further option is the SensLMicroFB series, which will be available in the firstquarter of 2013. These sensors are a very prom-ising alternative, as the devices will have an addi-tional fast output providing signals with a widthof O(ns) and provide a high PDE and gain. Meas-urements and simulation studies comparing thedifferent sensor types will be continued, in orderto find the devices which is best suited for thisapplication.

For the readout of the SiPMs, two different op-tions are currently discussed. One solution is todigitize the SiPM waveforms using the DRS chip.The waveforms then have to be further processedexternally, in order to determine the time-stamps.The second option is the STiC chip which includesa fast discriminator and a TDC digitizing the timeinformation. Details on both chips can be foundin chapter 13.

12.2 Simulation

Simulation studies using the full detector simula-tion described in section 15 have been carried outin order to determine the detector performance.

The optical properties of a tile are parameterizedusing a separate Geant4 simulation of a single tile.The SiPM simulation GosSiP [148] was used togenerate the signal waveforms from the hit inform-ation of the full detector simulation. The simu-lation has been done for a detector design with48 × 48 5 mm thick tiles per recurl station withBC420 scintillator and S10362-33-050 MPPCs.

Figure 12.2 shows the hit rate per tile as a func-tion of the position along the beam direction forphase II, including also tracks which pass severaltiles, as well as background events e.g. from thecollimators. These rates can be handled by theproposed readout electronics (see section 13). Inorder to further reduce the hit rate, and thereforethe signal pileup, optimizations like adjusting thetile angle to match the mean incident angle of thetracks are currently studied.

The time-stamps for the individual hits are as-signed using the signal waveforms generated bythe SiPM simulation. A simple fixed thresholdmethod is used which approximates the behaviourof the STiC chip. The same method can also beapplied to the output of the DRS chip.

The optimal threshold was determined to be≈ 10% of the mean signal amplitude (≈ 350pixels). Due to the varying signal amplitudes andthe fixed threshold, the individual time-stampshave to be corrected for the timewalk effect. Fig-ure 12.3 shows the timewalk as a function of theTime-over-Threshold.

ToT [ns]0 10 20 30 40 50

Tim

e-st

amp

- hit

time

[ns]

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4

5

Figure 12.3: Timewalk correction.

Figure 12.4 shows the distribution of the time-stamps relative to the true hit time given by thesimulation for phase II. A fit of a Gaussian func-tion yields a time resolution of σt = 45 ps. The

60


h_timingEntries 6094Mean 0.001942RMS 0.0748

/ ndf 2χ 259.7 / 103Constant 9.3± 524 Mean 0.000573± -0.000922 Sigma 0.00050± 0.04306

Time-stamp - hit time [ns]-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

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h_timingEntries 6094Mean 0.001942RMS 0.0748

/ ndf 2χ 259.7 / 103Constant 9.3± 524 Mean 0.000573± -0.000922 Sigma 0.00050± 0.04306

Figure 12.4: Timing for phase II. The timestampshave been corrected for timewalk.

non-Gaussian tails of the distribution come fromsignal pileup.

The efficiency for assigning a time-stamp to anisolated track within ±3σt of the true hit timeis ≈ 100%. Inefficiencies at the edge of a recurlstation, where a track deposits too little energy ina tile to pass the threshold can be neglected.

However, the efficiency is also influenced by sig-nal pileup. For the simple fixed threshold modelused in this analysis, an overall efficiency of ≈99.5% for phase I and ≈ 98.0% for phase II isachieved. With a more sophisticated peak-findingalgorithm, it should be possible to resolve pileupsignals which occur within a time interval of afew nanoseconds and consequently achieve an ef-ficiency of ≈ 100%. Also, using a SiPM with afast output, like the SensL MicroFB series, willsignificantly reduce the pileup and thus increasethe efficiency.

12.3 Time Resolution Measure-

ments

First measurements of time resolution of a single1×1×1 cm3 tile and a Hamamatsu S10362-33-050MPPC have been done using an oscilloscope witha bandwidth of 1 GHz. The scintillator materialused in this measurements is NE110. Comparedto BC420, this scintillator has a lower light yieldand a slightly slower rise and decay time; usinga more suited scintillator will thus improve theresults. The scintillation light was triggered usinga pulsed UV laser1.

Figure 12.5 shows the measured time resolu-tion as a function of the signal amplitude for athreshold of 10%. For a typical signal amplitudeof ≈ 350 pixels, a time resolution of ≈ 45 psis achieved, which is consistent with the simula-tion results. Figures 12.6 and 12.7 show the de-pendence on the applied threshold and SiPM biasvoltage.

These results show, that a time resolution wellbelow 100 ps can be achieved. It is expected, theresolution will not be degraded using the DRS orSTiC readout chip, which will be verified in futuremeasurements.

Signal amplitude [pixels]200 250 300 350 400 450 500 550

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Figure 12.5: Time resolution as a function of thesignal amplitude for a threshold of 10%. The amp-litude expected in the tile detector is ≈ 500 pixels.

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Figure 12.6: Time resolution as a function of thediscrimination threshold for 500 pixel signal amp-litude.

1The scintillator response to the UV light is a good ap-proximation of the response to electrons.

61


Operation voltage [V]70.4 70.6 70.8 71 71.2 71.4 71.6 71.8 72 72.2 72.4

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Figure 12.7: Time resolution as a function of theSiPM bias voltage for 500 pixel signal amplitudeand a threshold of 10%.

12.4 Detector Prototype

The design of a prototype of a tile detector mod-ule has been started (see Figure 12.1) and theconstruction is expected to be completed within2013. In this prototype the mechanical design ofthe support structures and readout infrastructurewill be tested and measurements of the detectorperformance will be carried out.

62

Chapter 13

Data Acquisition

1116 Pixel Sensors

up to 108

800 Mbit/s links

FPGA FPGA FPGA

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Collection

Server

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Gbit Ethernet

Figure 13.1: Mu3e readout scheme for the start-updetector.

13.1 Overview

The Mu3e data acquisition system works withouta hardware trigger on a push basis, i.e. the de-tector elements continuously send hit informationto the data acquisition (DAQ) system. The DAQconsists of three layers, namely front-end FPGAs,read-out boards and the filter farm. The topologyof interconnects is built such that every farm PC

gets to see the complete detector information fora select time slice. See Figure 13.2 for an over-view of the readout scheme and Figure 13.1 forthe scheme at detector start-up.

13.2 Occupancy

The bandwidth requirements of the data acquis-ition are largely determined by the expected de-tector occupancy, as all the Mu3e sub-detectorsproduce zero-suppressed output.

The occupancies shown are obtained with thefull simulation running at a muon stop rate of2 · 109 Hz (2 · 108 Hz for phase I) and pessimistic-ally estimating the beam related background byloosing another 4 · 109 Hz (4 · 108 Hz) of muonsalong the beam line. Figures 13.3 and 13.4 showthe expected number of hits per 50 ns frame inthe pixel detector. Figures 13.5 and 13.6 show thesame for the fibre detector. The distribution ofthe occupancy over the pixel sensors is shown inFigures 13.7 and 13.8.

13.3 Front-end

13.3.1 Pixel detector

The pixel sensors contain electronics for hit de-tection and time as well as address encoding. Allhits assigned to the same (20 MHz) time-stampconstitute a frame. The sensors collect the dataof 16 frames into a superframe and send it off chipvia an 800 Mbit/s low-voltage differential signal-ing (LVDS) link. The signals travel over a max-

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Figure 13.2: Overall Mu3e readout scheme

Number of silicon hits per frame0 100 200 300 400 500 600

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Figure 13.3: Number of pixel hits in the centraldetector per 50 ns frame in phase I running.

Number of pixel hits per frame0 500 1000 1500 2000 2500 30000

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Figure 13.4: Number of pixel hits in the completedetector per 50 ns frame in phase II running.

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Figure 13.5: Number of fibre hits per 50 ns framein phase I running.

Number of fibre hits per frame0 500 1000 1500 2000 2500 30000

2000400060008000

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Figure 13.6: Number of fibre hits per 50 ns framein phase II running.

ϕ0 2 4 6 8 10

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imum of 18 cm on a Kapton flex-print to the edgeof the sensitive area, where they are amplified bya driver chip. The Kapton prints then connects toa PCB located between the recurl layers and thebeam-pipe. On this PCB, up to 72 LVDS linksare fed into a FPGA. The FPGA provides buffer-ing and collects a long stream of frames (at least1024) into a frametrain. The assembled data arethen output to 8 3 Gbit/s links, such that the dataof one frame-train are sent on two links. On thePCB, the signals are converted to optical and sentoff-detector via fibres. An additional pair of op-tical links per FPGA is required for slow controland monitoring.

Hardware

The requirements for the on-detector FPGAs canbe met by mid- or even low-price devices (such as

65


Sensor Max Average Chip→FPGA Chip→FPGA Front end FPGA→ROChips Hits Hits link capacity total in Layer FPGAs capacity

/Chip /Layer Mbit/s Gbit/s Gbit/s

Layer 1 72 0.35 18.0 220 16 8 17Layer 2 108 0.25 18.4 157 17 8 17Layer 3 432 0.15 31.0 94 40 12 29Layer 4 504 0.15 28.6 94 47 14 27

Total 1116 96 120 42 90

Table 13.1: Pixel readout requirements (Phase IB without recurl stations).

Sensor Max Average Chip→FPGA Chip→FPGA Front end FPGA→ROChips Hits Hits link capacity total in Layer FPGAs capacity

/Chip /Layer Mbit/s Gbit/s Gbit/s

Layer 1 72 3.5 180 2203 155 8 166Layer 2 108 2.5 184 1574 166 8 170Layer 3 432 1.5 310 944 398 12 286Layer 4 504 1.5 286 944 465 14 264Recurl backward 1 inner 432 0.5 | 315 133 6 |Recurl backward 1 outer 504 0.5 | 315 155 7 |Recurl backward 2 inner 432 0.25 | 157 66 6 |Recurl backward 2 outer 504 0.25 | 157 77 7 |Recurl forward 1 inner 432 0.3 | 189 80 6 |Recurl forward 1 outer 504 0.3 | 189 93 7 |Recurl forward 2 inner 432 0.2 | 126 53 6 |Recurl forward 2 outer 504 0.2 Σ=490 126 62 7 Σ=452

Total 4860 1450 1903 86 1515

Table 13.2: Pixel readout requirements (Phase II), for the recurl stations only the sum of average hitsper layer and FPGA→RO capacity is given.

the ALTERA Cyclone IV family or the XILINXArtix VII family). The FPGAs are to be mountedon PCBs that are placed between the recurl layersand the beam-pipe.

Firmware

The main task of the on-detector FPGAs is col-lecting the relatively short time slices of 16 clockcycles assembled on the pixel chips to the long in-tervals treated by the individual filter farm PCs.During this buffering, the hits can be time orderedinside a slice and the protocol overhead can be re-duced. In addition, hits can be clustered.

A further task for the first line of FPGAs is theconfiguration and monitoring of the pixel chips.A 32 bit histogram of the hit counts in a singlesensor however requires 256 kB of memory, thusexceeding the capacity of the devices; an ex-

ternal memory interface would significantly in-crease the pin count and the PCB complexity; thehistograming task is thus deferred to the readoutboards.

These tasks are all fairly standard and FPGAsthat fulfill the bandwidth requirements for the in-and output channels do provide enough logic forimplementing them.

13.3.2 Timing detector

For the timing detectors, three readout schemesare currently under investigation: One based ona further development of the DRS switched ca-pacitor array developed at PSI, one based on theSTiC chip developed at KIP, Heidelberg Univer-sity and one with FPGA-based TDCs (mainly forthe fibres).

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Figure 13.8: Occupancy in 50 ns frames of the re-curl pixel sensors for phase II running. The axesenumerate sensor numbers.

DRS sampling readout

The readout of the tile and fibre detectors requireshigh rate capability and extremely good timingresolution. To achieve an overall detector tim-ing accuracy below 100 ps, the associated elec-tronics needs to be at least a factor of two bet-ter, i.e. 50 ps. The high rate environment causessignificant pile-up, which limits the usage of con-ventional techniques such as discriminators andTDCs. Therefore one option to read out the tilesis with the well-established waveform digitizingtechnology developed at PSI, which is in use sincemany years in the MEG experiment. It is basedon the DRS4 switched capacitor array, which iscapable of sampling the SiPM signals with up to 5Giga samples per second (GSPS) with a resolutionclose to 12 bits. It has been shown in the MEGexperiment that this technology allows a timingaccuracy in the order of 40 ps across many thou-sand channels. The knowledge of the exact wave-

form of an event is very well suited to detect andsuppress pile-up.

The tile readout electronics could be placed out-side the detector in special crates connected witha few meters of cable. This simplifies the designand maintainability, while not compromising thesignal quality dramatically.

A principal limitation arises from the DRS4chip, which is capable of only a limited event rateof about 100 kHz. While this will be sufficientfor Phase IB, it has to be improved for PhaseII. Therefore a new development has been star-ted to design a new version of this chip. TheDRS5 chip will use an internal analog memory(FIFO) to work in a dead-time less fashion up toan event rate of about 5 MHz. A critical part ofthe DRS5 chip which is the inverter chain oper-ating the sampling circuitry has already been de-signed in the new 110 nm CMOS technology andsubmitted. First test results are expected begin-ning of 2013. The dead-time less operation of thischip will be combined with higher sampling speed(10 GSPS) and a better timing accuracy, allowingfor a time measurement well below 10 ps.

In order to limit the amount of data to be readout, the FPGA connected to the DRS chip willalready analyze the waveform and extract its ma-jor parameters like time and amplitude. Only aprescaled subset of events will contain the full de-tector waveform in order to cross-check the ana-lysis algorithms in the FPGA. Methods have re-cently been published which obtain the timing in-formation by cross correlation or cubic interpol-ation with an accuracy of about 1/10th of thesampling interval, which would be 10 ps in the caseof 5 GSPS.

STiC readout

The STiC chip offers an alternative to the DRS5readout. STiC is a mixed mode 16-channel ASICchip in UMC 0.18 µm CMOS technology designedfor SiPM readout with high time resolution. Itis developed for Time-of-Flight measurements inhigh energy physics and medical imaging, in par-ticular the EndoTOFPET-US project. The chiphas a differential structure, however, it supportsboth differential and single-ended connection ofSiPMs. A 6 bit DAC allows to tune the voltageat each input terminal within ≈ 1 V. In this waythe SiPM operating voltage can be adjusted and

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Signal Wave

T Trigger

Edges processed by TDC

E trigger

Energy Threshold

Timing Threshold

Figure 13.9: Dual threshold discrimination for en-ergy and timing information.

temperature and device-to-device fluctuations canbe compensated.

The time and charge information of the signalare encrypted into two time-stamps which are ob-tained by discriminating the signal with two differ-ent thresholds (see Figure 13.9). The thresholdscan be tuned in a range of ≈ 0.2 − 15 pixel sig-nals for the timing and up to 200 pixel signals forthe charge. The time-stamps are then processedby an embedded TDC module with a resolutionof < 20 ps. A special linearization method is im-plemented to obtain a linear charge response in avery wide range. With the chip, a time-resolutionof ≈ 50 ps was measured for a 10 pixel signal ofa MPPC S10362-33-50 without scintillator. Fortypical signal amplitudes of O(100) pixels, whichare expected in the tile detector, the timing jitterof the chip is negligible.

The data rate of the current chip is limited to≈ 100 kHz per channel. However, the chip will bemodified to allow for data rates of ≈ 500 kHz perchannel within 2013/2014. Until 2016, the datarate will be further increased to several MHz inorder to match the requirements for phase II.

FPGA based readout

A further alternative for the fibre readout is theuse of time to digital converters implemented inFPGAs. Resolutions of O(1 ns) can be achievedfairly cheaply; much better performance requiresthe use of carry chain techniques, which greatlyreduces the number of channels per FPGA and

makes programming much more fickle. It has how-ever been shown that resolutions of O(10 ps) canbe achieved with this technology [149]. Whilstdefinitely not the optimal solution, FPGA basedtiming could serve as a low-cost, low-risk solutionfor phase IB running.

13.4 Read-out links

In total there are three different types of read-outlinks in the Mu3e data acquisition system. Thesame type of links can be used for a small num-ber of slow and fast control links in the oppositedirection.

The data from the MUPIX chips will be trans-mitted to the front-end FPGAs via LVDS linksat 800 Mbit/s, which is a quasi industry stand-ard. The fast serializers and LVDS drivers for theMUPIX chip will be adopted from a similar chipdesign by a group from Bonn [150]. The link willbe physically implemented as a matched differen-tial pair of aluminum traces on the sensor flex-print, shielded by ground lines on both sides. Itis foreseen to have a first set of LVDS repeatersjust outside the acceptance of the detector. Verycompact commercially available LVDS repeatershave already proven to be radiation tolerant. Out-side the acceptance, the flex-print will then be ofmultilayer type, with differential signal inner lay-ers, shielded by ground planes. The connection tothe PCB housing the front-end FPGA is made bysmall form factor connectors, which support highbandwidth. Lastly the routing on the front-endFPGA PCB will be done with matched differen-tial copper traces going to the pre-defined LVDSinputs of the FPGA itself.

There will be two types of optical high speeddata links. The first one is going from the front-end FPGAs to the read-out boards, the secondfrom the read-out boards to the FPGA PCIeboards in the event filter farm PCs. The opticallinks from the front-end FPGAs to the read outboards have a bandwidth of 3.125 Gbit/s, whichfits well the FPGA specifications. Each FPGA haseight (or more) fast transceiver blocks. The op-tical interface can be implemented using radiationtolerant components developed by the VersatileLink group [151]. Especially the 12-way laser ar-ray with MTP/MPO standard connector wouldgive a very compact form factor, the fall back solu-tion would be a radiation hard dual laser transmit-

68


ter system, the VTTx module developed at CERN[152]. The data laser will have a wavelength of850 nm and the optical fibre is of 50/125 multi-mode type, since this is a standard both in in-dustry and in particle physics detector readout.In the case of the 12-way emitter the fibres will goto a splitter and patch panel in order to combinefibres going to the same read-out board. In thecase of dual transmitters the fibres can be com-bined in groups of 12 using break-out fibre cables.The fibres traveling from the experimental areato the filter farm counting house can be furthercombined in cables containing 8 × 12 fibres goingto the same sub-farm. An optical patch panel foreach sub-farm will allow to connect the long dis-tance 96-fibre cables to 12 fibre patch cords goingto the readout boards. The readout boards have2 or 3 12-way optical inputs, which are populatedwith commercial receiver modules. The high-endFPGAs used on the read-out card have up to 66high speed transceiver blocks, which will be usedfor the de-serialization of the data.

The last type of link connects the read-out cardsto the FPGA PCIe boards in the event filter farmPCs. This optical link will be implemented as10 Gbit/s high speed link. Since each read-outboard is connected to every sub-farm PC with oneof the high speed links, they are point to pointsingle fibre links. The fibres are of 50/125 multi-mode type operated at 850 nm to stay compatiblewith the links from the detector. If 12-way opticaltransmitters and receivers running at 10 Gbit/scan be purchased, they will be used for this highspeed link. Otherwise single fibre transmittersand receivers will be used both on the read-outboard and the FPGA PCIe board side. In prac-tice the high speed optical receivers for the FPGAPCIe boards could be on optical mezzanines suchas the 8 channel St. Luce card developed by TUDortmund [153].

13.5 Read-out cards

The main tasks of the read-out cards is to act asswitches between the front end and the on-line re-construction farm and to act as buffers betweenthe synchronous front end and the asynchronousback end. The board design and choice of FP-GAs is dominated by the number of fast links re-quired. We plan to adapt an existing develop-ment, e.g. LHCb TELL1 cards [154] or PANDA

compute nodes [155], which would both fulfill ourneeds.

13.6 Event filter interface

The filter farm PCs will be equipped with FPGAcards in PCIe slots and optical receiver daughtercards, as described in more detail in section 14.2.

13.7 Data collection

The filter farm will output selected events at adata rate in the order of 50 MBytes/s in total.This data rate is low enough to be collected by asingle PC connected to the filter farm by com-mon GBit Ethernet and written to local disks.Then the data will be transferred to the centralPSI computing center, where it is stored and ana-lyzed. For the central data acquisition the wellestablished MIDAS (Maximum Integrated DataAcquisition System) [156] software package willbe used. This software is currently used in severalmajor experiments such as the T2K ND280 de-tector in Japan [157], ALPHA at CERN and theMEG experiment at PSI [158]. It can easily handlethe required data rate, and contains all necessarytools such as event building, a slow control systemincluding a history database and an alarm system.A web interface allows controlling and monitoringthe experiment through the Internet. The farmPCs will use MIDAS library calls to ship the datato the central DAQ PC. The framework also offersfacilities to send configuration parameters from acentral database (the “Online DataBase” or ODB)to all connected farm PCs and to coordinate com-mon starts and stops of acquisition (run control).

For the purpose of monitoring and data qual-ity control of the experiment the MIDAS systemoffers taps to the data stream for connections ofanalysis and graphical display programs. The out-put of graphical user interface programs can be fedback into the web interface of the MIDAS systemso the experiment can be monitored also remotelywith just a Web browser.

13.8 Slow control

The slow control system deals with all “slow” datasuch as high voltages for the SiPMs and siliconsensors, ambient temperatures and pressures. For

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Figure 13.10: SCS-2001 unit as part of theMSCB slow control system. This unit has 64 in-put/output channels, which can be configured viaplug-in boards as digital or analog channels. Manyplug-in boards exist already such as PT100 tem-perature sensor readout cards, analog high resol-ution inputs (24 bit resolution), valve control out-puts and many more.

the configuration and control of the silicon pixelsensors the JTAG standard [132] will be used. Itis planned to use the MIDAS Slow Control Bus(MSCB) system [159] to link all distributed con-trol and monitoring devices into a single system.The MSCB system is also well established at sev-eral laboratories. It uses a serial differential busfor communication, and simple micro controllersin all control devices. The micro controllers per-form local control loops such as high voltage sta-bilization, and send measured values to the cent-ral DAQ system for monitoring. Many devicesalready exist for this system, such as the SCS-2001 unit shown in 13.10. Since the system was

developed at PSI, it can be quickly adapted tonew hardware. The high voltage control for theSiPMs can for example be directly integrated intothe carrier boards holding the SiPMs, thus elim-inating the need for high voltage cables. The op-timized protocol of the MSCB system allows themonitoring of many thousand channels with re-petition rates in the 100 ms range, which will bemore than enough for this experiment.

In addition to the MSCB system, the MIDASslow control package contains interfaces to the PSIbeamline elements via the EPICS system [160].This allows monitoring and control of the beam-line from the main DAQ system, which has beenproven very versatile in other experiments usingthis scheme.

All slow control data will be stored in the his-tory system of the MIDAS system, so that longterm stabilities of the experiment can be effect-ively verified. The slow control data is also fedinto the main event data stream, so that any off-line analysis of the event data has this data avail-able.

A special case is the configuration of the pixeldetectors, which require many million parameters,like the trim-DAC values for each pixel. Since theamount of data here is considerably larger than forall other systems, an extension of the slow controlsystem is planned. A dedicated program manages,visualizes and exchanges the pixel detector con-figuration parameters between an optimized data-base and the pixel hardware. In this way the timerequired to configure the pixel detectors can beminimized, while this program is still connectedto the main DAQ system. It can be synchronizedwith run starts and stops, and can inject pixelmonitoring data periodically into the event datastream for offline analysis.

70

Chapter 14

Online Event Selection

14.1 Selection Algorithms

As in the final analysis, event selection in the filterfarm can rely on the coincidence of three tracks intime and vertex and on their kinematics. Espe-cially for high rate running, coincidence in timein the fibre detector is not sufficient to reduce thedata rate by three to four orders of magnitude.Thus a track reconstruction will be required. Thetriplet based multiple scattering fit described inchapter 16 is well suited for online implementa-tion and current GPUs can perform 109 tripletfits per second1, thus already fulfilling the needsof Mu3e up to at least medium intensity (few 108

muons/s) running.Triplets of the tracks thus reconstructed can

then be fit to a common vertex. Even loose ver-tex requirements can give a 103 reduction factorat 2 · 109 Hz muon rate and 104 − 105 for thephase I experiment (see Figures 14.1 and 14.2).Combining the vertexing with modest kinematicrequirements (e.g. on the three-particle invariantmass or the planarity) should produce the requireddata reduction, leaving the timing information asa valuable offline cross-check (and obviating theneed for online timing reconstruction).

14.2 Hardware Implementation

The data will arrive on the farm PCs via op-tical links on a PCIe FPGA board. The FPGAwill perform the event building and buffering and

1As tested on a AMD Radeon 6990 using OpenCL underLinux.

also allows to run simple clustering and sortingalgorithms. The event data are then transferredvia DMA over the PCIe 3 bus2 to the memory ofa graphics processing unit (GPU), where the se-lection algorithms are run. The GPU then postsselected events and monitoring data to the mainmemory of the PC, from where the CPU shipsit via Ethernet to the central data acquisitioncomputer running the MIDAS software. At thatcomputer, the data streams from the farm PCsare combined into a single data stream, combinedwith various slow control data, compressed andstored.

For the receiver FPGA cards, evaluation boardsfrom either XILINX [161], or ALTERA (Fig-ure 14.3) [162,163] or similar hardware built by thecollaboration could be used in conjunction withdaughter boards with the optical receivers (sim-ilar to e.g. the optical receiver boards used in theLHCb readout electronics [164]). The maximumdata rate over the PCIe 3.0 bus is 16 Gbyte/s,amply sufficient for phase I3. For the full phase IIrate, the raw link speed is still sufficient, wouldhowever have to be fully and efficiently used. ThePCIe 4.0 standard, doubling this rate, should be-come commercially available around 2017, com-patible with phase II running; alternatively, thenumber of farm PCs could be increased.

2Note that PCIe is actually not a bus protocol, butoffers switched point-to-point connections. The bus desig-nation is due to the software-side backwards compatibilityto the original PCI bus interface.

3For phase I running, the FPGA-GPU link can also beimplemented on PCIe 2.0 (max. 8 Gbyte/s), which is bettersupported on currently available FPGAs.

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Figure 14.2: Fraction of 50 ns frames containingthree vertices consistent with e+e−e+ inside agiven distance for a muon stop rate of 2 · 109 Hz for680’000 simulated frames. In the top plot, everycrossing of a simulated electron/positron track iscounted as a vertex; charge assignments are madepurely on the apparent curvature, i.e. recurlingpositrons are counted as electrons. In the bottomplot, only true electrons are counted.

Figure 14.3: ALTERA Stratix IV PCIe develop-ment board.

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The GPU boards will be obtained commerciallyas late as possible in order to profit from the fastdevelopments and sinking prices. As far as rawfloating point throughput is concerned, currenthigh-end GPUs already pack enough power forhigh rate running [165,166]. Newer cards are how-ever expected to offer higher memory bandwidthand better caching. Also the performance of thedriver software (especially as far as the PCIe 3 busis concerned) and the GPU compilers is expec-ted to improve. The two GPU vendors AMD andNVIDIA offer fairly different architectures; whichone performs better depends a lot on the details ofthe algorithm to be implemented; we are currently

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performing tests with both architectures and willchoose a vendor once we have a mature imple-mentation.

We currently plan to host the farm PCs in in-dividual tower casings, ensuring enough space for

the FPGA board and the high end GPU whilstallowing for air cooling. At load, each tower willconsume around 0.5 KW, so adequate cooling ofthe counting house is essential.

73

Chapter 15

Simulation

This chapter describes the Geant4 [124, 167]based simulation used to derive the figures andplots in this proposal.

15.1 Detector geometry

15.1.1 Beam delivery

In the simulation, the beam is started 3 m infront of the target inside a beam transport solen-oid. Beam particles are generated with a profileand momentum spectrum like the one observed inMEG. 1.5 m before the target, the beam enters themain solenoid and shortly before the target it exitsthe beam vacuum through a thin window. Alongthe beamline, two thick lead collimators reducethe beam to the target size. For an overview ofthe simulated beamline elements, see Figure 15.2.In this simple setup, about a third of the gen-erated muons decay in the target, which, whilst

Figure 15.1: Wire frame view of the simulateddetector.

not very efficient, gives a conservative estimate ofbeam-induced backgrounds.

15.1.2 Target

The target is simulated as a hollow aluminiumdouble cone supported by three nylon strings ateach end and a nylon string along its axis, see alsochapter 9.

15.1.3 Pixel detector

The pixel detector is simulated as 50 µm of sil-icon on top of 15 µm of aluminium representing thetraces on the flexprint (covering half the availablearea) on top of 50 µm of Kapton, with the siliconoffset such that an overlap with next sensor is cre-ated, see Figure 15.4. Half a millimeter of the pixelsensor at the edge is assumed to be inactive, therest is divided into 80 × 80 µm2 pixels. The sim-ulated sensor layers are supported at their endsby plastic and aluminium structures modeled onthose in the mechanical prototype shown in Fig-ure 10.20.

15.1.4 Scintillating fibres

The fibre detector is simulated as three circularlayers of 250 µm scintillating fibres in the mainsimulation. A detailed simulation including op-tical transport and the effect of fibre cladding andcoating also exists, see section 11.3. The results ofthe detailed simulation regarding light yield andpropagation times will eventually be fed back intothe main simulation in a parameterized form. The

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100 mm

Figure 15.3: Geometry of the detector in the simulation. The top half only shows active (sensor)volumina, whereas the bottom half only shows support structures.

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10 mm

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Figure 15.4: Pixel detector simulation geometryfor the innermost layer. The sensor is shownin black, the aluminium traces in blue and theKapton support in orange. Note that all thick-nesses are stretched by a factor of 2.

response of the silicon photomultipliers is simu-lated by the GosSiP package [148]. In the simu-lation, the fibres are supported at both ends bymassive aluminium rings.

15.1.5 Tile detector

The simulated tile detector consists of plastic scin-tillator tiles mounted on an aluminium tube. Alsohere, a separate detailed simulation including lighttransport and silicon photomultiplier response isavailable and will have to be fed back into themain simulation in a parameterized form.

15.2 Magnetic field

The simulated magnetic field can be read fromarbitrary field maps or generated in the code viaintegration over current loops. The propagationof muons in the field includes spin tracking. Forthe simulations shown in this report, the field wasgenerated from 100 current loops spaced equallyover 3 m, with currents normalized such that thelongitudinal component of the field in the centerof the target is 1 T, supplemented by a 1.5 T fieldin the center of the beam transport solenoid, seesection 15.1.1 and Figure 15.2.

15.3 Physics Processes

15.3.1 Multiple Coulomb scattering

Multiple coulomb scattering is the main limitingfactor for the resolution of the experiment; an ac-curate simulation is thus crucial. The best res-ults are obtained by simulating each individualscattering, which however results in prohibitivelylarge computing times. A large selection of mul-tiple scattering parameterizations are available in

Geant4; in a test setup they were compared to thesingle scattering model, see Figure 15.5. The bestoverall description is obtained from the Urbán-Model [168] at large step widths, which also hasthe shortest computation times. In the helium gason the other hand, none of the parameterizationsperforms adequately, see Figure 15.6.

We plan to verify the simulation results withbeam telescope measurements in 2013, whichshould also lead to a usable parameterization ofmultiple scattering in gases.

15.3.2 Muon decays

Michel decay

Geant4 implements the Michel decay including po-larization of both the muon and the positron basedon [169] and [170]. The spectra of the neutrinosdo not follow the physical distribution, this doeshowever not affect the simulation for Mu3e. Some-what more worrying is the fact that the Michelmatrix element contains radiative corrections butis not clearly separated from the radiative decaymatrix element.

Radiative decay

The radiative decay of the muon was implementedin Geant4 by the TWIST collaboration [171] basedon [172]. The code does not describe the neutrinospectra and avoids the collinear and infrared sin-gularities by sampling the matrix element assum-ing a finite integral.

Radiative decay with internal conversion

The radiative decay with internal conversion issimulated using the hit and miss technique onevents generated evenly in phase space using theRAMBO code [173] and applying the matrix ele-ment from [116]. Unfortunately, there is currentlyno polarized version of the matrix element avail-able and thus the simulation is unpolarized. Thehit and miss technique is very expensive in termsof computation time, if the complete phase spaceis to be simulated (as the matrix elements variesby more than 16 orders of magnitude), this canhowever be overcome by restricting the simulationto regions of particular interest, e.g. high invariantmasses of the visible particles.

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1003

10·

Figure 15.5: Comparison of multiple coulomb scattering models in different scattering angle ranges. Thescatterer is a single silicon-Kapton assembly shot at at a right angle with 30 MeV positrons. The blackdots and the green line show the single scattering model which serves as a reference; as expected, thesingle scattering model is not affected by the Geant step size. Of all the parameterizations, the Urbánmodel with a step size that treats each bit of material as a single volume performs best.

)ϑ (

0.5 1 1.5 2 2.5 30

100

200

300

400

500

600

700

800

900

1000










)ϑ (

0.15 0.2 0.25 0.3 0.35 0.4 0.450

1000

2000

3000

4000

5000

6000

)ϑ (

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Figure 15.6: Comparison of multiple coulomb scattering models in m of helium gas for different scatteringangle ranges. The test particles are 30 MeV positrons. The black dots and the green line show the singlescattering model which serves as a reference. All the parameterizations are unfortunately inadequate.

77


Figure 15.7: View of a simulated frame.

Signal

The signal kinematics are highly model-dependent, see chapter 4. If not otherwisenoted, we have used three particle phase spacedistributions in the simulation, following thepractice of SINDRUM and earlier experiments.

Special decays

The simulation allows the simulation of overlapdecays, where we force more than one muon decayto happen at a single vertex. Thus we can simu-late the accidental backgrounds arising e.g. fromthe overlap of an internal conversion decay and aMichel decay without having to generate in excessof 1016 frames.

15.4 Time structure

As the Mu3e experiment operates with a quasicontinuous beam, the paradigms of bunch cross-ing and event from collider experiments do notapply; they have however informed the design ofthe Geant4 package. In our simulation, particlesare assigned a 64 bit ID, which is unique overa run and thus conserves identities and mother-daughter relationships across the boundaries ofread-out time frames. Before each step of track-ing the particle through the detector, it is checkedwhether the particle has just crossed into the nexttime slice. If so, its information is stored, itstime relative to the time slice adjusted and track-ing deferred to the next slice. Thus we ensurethat we correctly treat muons stuck in the tar-get before decaying and decay products crossingread-out frame boundaries while traversing the de-tector. In order to simulate a steady state, whereapproximately the same number of muons enterthe target and decay, the first 5 ms of simulationrunning, during which the target is loaded, areusually thrown away and not used in occupancyor efficiency studies.

Currently not simulated are effects of the40 MHz structure of the primary proton beam onthe time structure seen in the detector; if thiswould be needed, a measured structure could eas-ily be superimposed on the generation of muonsin the simulation framework.

78

Chapter 16

Reconstruction

16.1 Track Reconstruction in the

Pixel Tracker

A precise track reconstruction of electrons is ofhighest importance for the identification of theµ → eee decay with a sensitivity of 1 out of1015 (1016) ordinary Michel decays in phase I (II),which have to be suppressed by 16 orders of mag-nitude.

Due to the high rate and the resulting high oc-cupancy especially at phase II of the project withup to 100 tracks per readout frame, the recon-struction algorithm has to deal effectively withthe combinatorial background in order to reducethe fake rate, i.e. the rate of wrongly reconstruc-ted tracks, to an acceptable level. The combin-atorial problem is not only due to the high ratebut also due to the large bending of the low mo-mentum electrons in the strong magnetic field ofB = 1 T, which, depending on the position andflight direction can make several turns in the de-tector (recurlers). Hit combinations can span overdistances of more than half a meter. Hits of re-curling tracks are found on opposite sides of thedetector and still have to be correctly combined bythe reconstruction program. This is of particularimportance for the determination of the flight dir-ection and therefore charge of the particle. Onlyfor a fully reconstructed track the time informa-tion provided by the time of flight system can becorrectly applied.

As the full detector readout is triggerless,all muon decays have to be fully reconstructedalready on filter farm level, setting high demands

on the speed of the online track reconstruction al-gorithm. A further complication comes from thefact that the track resolution is dominated by mul-tiple scattering in the silicon pixel sensors and notby the pixel size, in contrast to most other exper-iments. Therefore, standard non-iterative circlefits of tracks [174] as used in high energy experi-ments can not be used here.

In order to reduce multiple scattering, thenumber of sensor layers are reduced to a min-imum in the detector design which, unfortunately,also reduces redundancy for track reconstruction.Therefore, the track reconstruction also has tocope with a minimum of information provided byonly four sensor layers.

16.2 Track Fitting and Linking

For the track reconstruction two different ap-proaches are followed in the Mu3e experiment, thebroken line fit [175, 176] and the fast linear fitbased on multiple scattering [177]. The brokenline fit determines hit positions and scatteringangles simultaneously and was implemented in 2D[175, 178] and recently also in 3D [176, 179]. Itis based on linearisation of a previous circle fit,works non-iteratively and provides the correlationbetween all fit quantities. The broken line fit,however, requires knowledge of the assignments ofhits to tracks from a previous linking step. There-fore, the broken line fit can only be used in thefinal step of the track reconstruction, also becausea previous track fit is required for the linearisationprocedure.

79


ΦMS

R1 R2

s01

x0 x2

x1

c2 c1

Φ2

ΦMS

1Φ

d 01φ01

d 12

φ12

s12

y

x

Figure 16.1: Sketch of the variables used in themultiple scattering fit.

Track polar angle0 0.5 1 1.5 2 2.5 3

0

200

400

600

800

1000

8 of 8 hits

7 of 8 hits

6 of 6 hits

5 of 6 hits

4 of 4 hits

Figure 16.2: Track types versus track polar anglefor Michel decays in phase IA.


0

200

400

600

800

1000

8 of 8 hits

7 of 8 hits

6 of 6 hits

5 of 6 hits

4 of 4 hits

Figure 16.3: Track types versus track polar anglefor Michel decays in phase IB.

The fast three-dimensional multiple scattering(MS) fit [177] is based on fitting the multiple scat-tering angles at the middle hit position in a hittriplet combination, see Figure 16.1. In this fit,spatial uncertainties of the hit positions are ig-nored. This is a very good approximation for theMu3e experiment as the pixel resolution uncer-tainty given by σpixel = 80/

√12 µm is much smal-

ler than the uncertainty from multiple scatteringin the corresponding sensor layer. The MS-fit re-quires a detailed knowledge of the material distri-bution in the detector for the calculation of thescattering angle uncertainty. It minimises the azi-muthal and polar scattering angles at the sensorcorresponding to the middle hit and exploits en-ergy conservation1. The hit triplet trajectory, rep-resented by two connected helical curves, is de-scribed by the following two equations:

sin2 Φ1

2=

d201

4R23D

+z2

01

R23D

sin2 (Φ1/2)

Φ21

(16.1)

sin2 Φ2

2=

d212

4R23D

+z2

12

R23D

sin2 (Φ2/2)

Φ22

.(16.2)

The quantities, also shown in the sketch of Fig-ure 16.1, are the following: R3D is the three di-mensional track radius, which can be directly re-lated to the momentum of the particle for a givenmagnetic field; Φ1 (Φ2) are the bending angles ofthe first (second) arc and d01 (d12) and z01 (z12)are the distances between the hits in the planetransverse and longitudinal to the solenoidal mag-netic field between the first and second (second

1the energy loss in the Mu3e experiment is only about80 keV per sensor layer and can be neglected for track find-ing.


0

200

400

600

800

1000

8 of 8 hits

7 of 8 hits

6 of 6 hits

5 of 6 hits

4 of 4 hits

Figure 16.4: Track types versus track polar anglefor Michel decays in phase II.

80


Hits fitted per track

0 1 2 3 4 5 6 7 8 9

310

410

Reconstructed Momentum [MeV/c]

0 10 20 30 40 50 60

1

10

210

310

Rec. Momentum - Gen. Momentum [MeV/c]

-3 -2 -1 0 1 2 3

210

310

410

RMS: 0.73 MeV/c

Reconstructed track polar angle

0 0.5 1 1.5 2 2.5 3

1

10

210

310

Figure 16.5: Tracking performance for Michel decays in phase IA.

and third) hit, respectively. These equations canbe linearised and solved in a fast non-iterative pro-cedure [177].

This linearized MS-fit is used as basis for thefull reconstruction of tracks in the pixel detector.Tracks with more than three hits are fitted by sub-sequently combining several hit triplets. In thecurrent reconstruction program [180], long trackscombining hits from several pixel layers are recon-structed first, then shorter tracks with fewer hitassignments are reconstructed. This procedure isrepeated until no hits are left or no further tracksare found. Tracks with unresolved hit ambiguitiesare ignored in the following study to ensure highquality tracks with low fake rate. Also tracks withless than four hits combined are ignored.

The number of hits linked to tracks depends onthe single hit efficiency, which is assumed to be98% in the following studies, on the track direction(polar angle), the geometry of the pixel trackerand the geometrical acceptance of the detector,

which is largest in phase II with four recurl sta-tions. The multiplicity of linked tracks as functionof the polar angle is shown in Figures 16.2, 16.3and 16.4 for the three different detector configura-tions. The multiplicity of linked hits is highest inthe central region of the detector, where recurlingtracks can be fully reconstructed. In the currentversion of the reconstruction program, only singleturns of tracks are reconstructed, correspondingto a maximum of eight hits - four hits assigned tothe outgoing trajectory and four hits assigned tothe returning trajectory. In cases where one hit ismissing, only seven hits are linked. For upstreamor downstream going tracks the recurlers are notfully reconstructed, leading to tracks with mainlyfour linked hits or six linked hits depending onthe detector setup and the number of implemen-ted recurl stations. It should be noted here thatthere is a big qualitative difference between thefour-hit tracks and tracks with more than 4 hits(recurlers). The bending radius of recurling tracks

81



0 1 2 3 4 5 6 7 8 9

310

410


0 10 20 30 40 50 60

1

10

210

310


-3 -2 -1 0 1 2 3

10

210

310

410RMS: 0.44 MeV/c


0 0.5 1 1.5 2 2.5 3

1

10

210

310

Figure 16.6: Tracking performance for Michel decays in phase IB.

can be measured with much higher precision dueto the larger bending in the magnetic field. Thisleads to very different momentum resolutions forthe different detector setups.

In phase IA without Recurl Stations most tracksare reconstructed with only four linked hits. Thisyields a momentum resolution for reconstructedMichel electrons of about RMS(p) = 0.73 MeV/c,see Figure 16.5. This resolution improves consid-erably to RMS(p) = 0.44 MeV/c by adding twoinner Recurl Stations in phase IB (Figure 16.6)and it improves further to RMS(p) = 0.28 MeV/cby adding two inner and two outer Recurl Sta-tions in phase II Figure 16.7). The reconstructionof the recurling tracks, which provide high resol-ution momentum information, is crucial for thesuccess of the experiment.

16.3 Vertex Fitting

A vertex fit will be used to precisely reconstructthe position of the muon decay for signal events.The vertex fit intrinsically checks the consistencyof the assumption that all three signal candidatetracks originate from the same vertex. A commonvertex fit of the three candidate electrons allowsa suppression of the combinatorial background ofMichel decays by a factor of about 3 · 108 due tothe very good pointing resolution of the pixel de-tector, which is mainly given by the multiple scat-tering at the first sensor layer. Instead of usinga common vertex fit, also the distance betweentarget impact points of reconstructed and extra-polated tracks can be used to discriminate signalagainst background. For simplicity the latter ap-proach is used here for the following sensitivitystudy.

82



0 1 2 3 4 5 6 7 8 9

310

410


0 10 20 30 40 50 60

1

10

210

310


-3 -2 -1 0 1 2 31

10

210

310

410 RMS: 0.28 MeV/c


0 0.5 1 1.5 2 2.5 3

1

10

210

310

Figure 16.7: Tracking performance for Michel decays in phase II.

83

Chapter 17

Sensitivity Study

Figure 17.1: Hits in a simulated event at 2 · 109 Hzmuon rate, viewed in the plane transverse to thebeam.

A sensitivity study based on a full simulationof the pixel detector is performed to estimate thebackground contribution at the different phases ofthe Mu3e experiment. The simulation includes afirst material description of the detector, whichvaries between the different detector phases. Theincreasing level of detector instrumentation atlater stages of the experiment will provide moreinformation for particle tracking on one hand.On the other hand, the scintillating fibre tracker,which will be added at a later stage of the exper-iment when running at high muon rates, will also

add multiple scattering and consequently increaseconfusion in the track linking step. In addition,the factor 10 and 100 higher increased particlerates at the Phase IB and II, respectively, will sig-nificantly increase the combinatorial backgroundfrom Michel decays and other accidentals. A de-tailed simulation is therefore required to estimatedthe sensitivity reach of the different experimentalphases. The simulated setups are summarized inTable 17.1.

17.1 Simulation and Reconstruc-

tion Software

In order to estimate the maximum achievablesensitivities at the different stages of the projectthe track reconstruction program [180] is inter-faced to a) a full GEANT simulation of the de-tector and b) to a fast simulation program, whichis mainly used for the following sensitivity studies.Both simulations were cross checked to give com-parable values for the track parameter resolution.

In a first test it was proven that the track re-construction program is relatively insensitive withregards to changes of the single hit efficiency. Us-ing tight reconstruction criteria it is found thata 5 % loss of signal hits corresponds to an about5 % loss of tracks and an about 10 % loss of signalevents.

Noise hits also affect the track reconstruction.From noise studies of the MUPIX2 prototype chipit is known that the noise rate is very small (nonoise hits were observed in an overnight run ata low threshold). To simulate the effect of noise

84


Phase IA Phase IB Phase II

Recurl stations 0 2 4Scintillating fibres No Yes YesCharge measurement No Yes YesTarget stopping rate1 (Hz) 2 · 107 2 · 108 2 · 109

Table 17.1: Mu3e configurations considered for the sensitivity studies. Note that the detector acceptanceis about. 50 % for signal events, given by the geometry of the central pixel detector.1 Highest possible rates are assumed in the simulation in order to be conservative.

100 additional hits are randomly generated in thepixel detectors, corresponding to a noise rate of10−6 Hz per pixel. This rate will be remeasuredas soon as a first large scale detector including afull readout chain becomes available.

17.2 Signal Acceptance

Signal events are generated by using a constantmatrix element in phase space. This choice ismotivated by LFV models with effective four-fermion contact interactions, which predict a con-stant matrix element. The so generated signalevents are used for the following efficiency stud-ies.

The resulting signal efficiency is mainly givenby the acceptance of the experiment, which is intotal about 50 % for the innermost detector lay-ers being placed at radii of approximately 2.0 cmand 3.0 cm. The total acceptance consists of twocontributions, one related to the orientation of thedecay plane with respect to the instrumented re-gions of the experiment and one from the min-imum bending radius (momentum), which can bereconstructed in the experimental setup.

By moving the inner pixel layers closer to thetarget, the total acceptance can be slightly in-creased to about 55 %. Further improvements ofthe total acceptance to about 60 % or more areonly possible by using a longer inner barrel designand by reconstructing particles with a lower mo-mentum threshold. The latter can be achieved intwo ways - a) by including highly bent trajectoriesin the track reconstruction or b) by decreasing thestrength of the magnetic field, which however alsocompromises the momentum resolution.

In the following, a conservative design is chosenwith inner sensor layers placed at 2.0 and 3.0 cmand outer sensor layers placed at 7.0 and 8.0 cm,providing a signal acceptance of about 50 %.

The resulting mass resolutions calculated fromthe reconstructed track parameters are shown inFigures 17.2-17.4 for the different phases. Com-pared to phase IA, the mass resolutions improveconsiderably by adding the recurl stations atphase IB and phase II and yield - despite the addi-tional material from the scintillating fibre tracker- resolutions well below 1 MeV. Of special import-ance for the background suppression is the strongreduction of the tails in the phase II setup.

17.3 Selection

17.3.1 Kinematic Selection of SignalEvents

The mass resolution can be further improved byrejecting badly reconstructed signal events, whereone or several tracks are either wrongly recon-structed or suffer from large multiple scattering.A wrong measurement of the track momentum ordirection affects momentum balance and leads toa measurable missing momentum. In the follow-ing we follow the strategy of the SINDRUM ex-periment [15] and define an acoplanar momentumvector pacopl, which is obtained by projecting thevectorial sum of all track momenta into the decayplane defined by the three tracks. The correlationbetween the reconstructed invariant mass and thevariable pacopl is shown in Figures 17.5. In ad-dition to the main spot at small values of pacopl,which originates from well measured signal events,two diagonal sidebands originating from wronglymeasured signal events are visible. By applyingthe cut pacopl < 1.4 MeV/c, which will also be usedto reject background events in the following, mostof the wrongly measured signal events are rejec-ted.

The resulting mass resolution plots are shown inFigure 17.6-17.8, which show by about 20 % im-

85


proved resolutions and significantly reduced tails.The expected mass resolutions and signal efficien-cies for the three stages of the experiment are sum-marized in Table 17.2.

The main criterion for the kinematic selection ofsignal events is the reconstructed invariant mass.In a final analysis the number of signal and back-ground events will be determined by a fit of theinvariant mass distribution, see also Figures 17.12-17.14 or by exploiting multivariate methods whichinclude several estimators. For sake of simplicitythe number of signal events is here determinedfrom a 2-sigma mass window around the nominalmuon mass.

17.3.2 Reduction of the µ → eeeνν Back-ground

The acoplanar momentum cut is also very effect-ive in reducing the dominating background fromradiative events with internal conversion µ →eeeνν. These events are characterized by miss-ing energy carried away by the two undetectedneutrinos. Most of these background events haveeither a small value of the reconstructed three elec-tron mass meee or show some momentum imbal-ance. In particular the class of dangerous back-ground events, which have only little missing en-ergy, carried away by the two neutrinos, and arewrongly reconstructed such that the reconstruc-ted invariant mass matches the muon mass, showsome significant momentum imbalance. Most ofthese background events are rejected by the cutpacopl < 1.4 MeV/c.

The separation of signal and background in theplane pacopl versus meee is shown for the threestages of the experiments in Figures 17.9-17.11. Aclear separation of signal and background eventsat a level of 10−17 − 10−16 muon decays is vis-ible. This separation improves with the upgradedexperiment at phase IB and II.

The projected invariant mass distribution of sig-nal and background after applying the acoplanarmomentum cut is shown in the Figures 17.12-17.14. Theses distributions are used as basis forthe estimated sensitivity calculation.

17.3.3 Reduction of Accidental Back-ground

The dominant contribution to the accidental back-ground comes from combinatorial background of

]2Reconstructed Mass [MeV/c102 103 104 105 106 107 108 109 1100

100

200

300

400

500

6002RMS: 1.12 MeV/c2: 0.48 MeV/c1σ2: 1.38 MeV/c2σ2: 0.81 MeV/cavσ

Figure 17.2: Reconstructed mass resolution forsignal events in the phase IA configuration.


200

400

600

800

1000

1200

1400 2RMS: 0.65 MeV/c2: 1.17 MeV/c1σ2: 0.38 MeV/c2σ2: 0.44 MeV/cavσ

Figure 17.3: Reconstructed mass resolution forsignal events in the phase IB configuration.


200

400

600

800

1000

1200

1400

1600


Figure 17.4: Reconstructed mass resolution forsignal events in the phase II configuration.

86



Michel decays:Efficiency (unpolarized) 50.0 % 53.4 % 52.4 %Momentum RMS 0.73 MeV/c 0.44 MeV/c 0.28 MeV/cWrong charge fraction 1.14 % 0.45 % 0.45 %

Signal:Reconstruction efficiency 39 % 46 % 48 %Energy sum RMS (reconstructed) 1.12 MeV/c2 0.65 MeV/c2 0.52 MeV/c2

Efficiency after selection 26 % 39 % 38 %Energy sum RMS (selected) 0.91 MeV/c2 0.47 MeV/c2 0.42 MeV/c2

Track dca resolution (σ) 190 µm 185 µm 185 µm

Table 17.2: Efficiencies and resolutions used in the sensitivity study. dca is the distance of closestapproach of a track to the beam line. The drop in the efficiency after selection for phase II is due to thelarger combinatorial background.


Aco

plan

ar M

omen

tum

[MeV

/c]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure 17.5: Reconstruced mass versus acoplanarmomentum for the phase II detector.


50

100

150

200

250

300

350

400

450


Figure 17.6: Reconstructed mass resolution forsignal events after kinematic cuts in the phase IAconfiguration.


200

400

600

800

1000


Figure 17.7: Reconstructed mass resolution forsignal events after kinematic cuts in the phase IBconfiguration.


200

400

600

800

1000

1200

1400


Figure 17.8: Reconstructed mass resolution forsignal events after kinematic cuts in the phase IIconfiguration.

87


]2Reconstructed Mass [MeV/c

102 103 104 105 106 107 108 109 110

Aco

pla

na

r M

om

en

tum

[M

eV

/c]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1510·

Figure 17.9: Internal conversion background (col-ours) and signal (black dots) in the acoplanar mo-mentum - reconstructed mass plane for the phaseIA detector configuration.


102 103 104 105 106 107 108 109 110

Aco

pla

na

r M

om

en

tum

[M

eV

/c]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1510·

Figure 17.10: Internal conversion background(colours) and signal (black dots) in the acoplanarmomentum - reconstructed mass plane for thephase IB detector configuration.


102 103 104 105 106 107 108 109 110

Aco

pla

na

r M

om

en

tum

[M

eV

/c]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-1510·

Figure 17.11: Internal conversion background(colours) and signal (black dots) in the acoplanarmomentum - reconstructed mass plane for thephase II detector configuration.

]2Reconstructed Mass [MeV/c101 102 103 104 105 106

Eve

nts

per

muo

n de

cay

and

0.1

MeV

-2010

-1910

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110

-1010 generatedνν eee→ µ simulatedνν eee→ µ

-12Signal BF 10-13Signal BF 10-14Signal BF 10-15Signal BF 10-16Signal BF 10-17Signal BF 10

Figure 17.12: Tail of the internal conversion distri-bution overlaid with signal at different branchingratios for the phase IA detector. The resolutionfor the internal conversion decays was taken from30 000 simulated signal decays.


Eve

nts

per

muo

n de

cay

and

0.1

MeV

-2010

-1910

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110



Figure 17.13: Tail of the internal conversion distri-bution overlaid with signal at different branchingratios for the phase IB detector. The resolutionfor the internal conversion decays was taken from30 000 simulated signal decays.

88



Eve

nts

per

muo

n de

cay

and

0.1

MeV

-2010

-1910

-1810

-1710

-1610

-1510

-1410

-1310

-1210

-1110



Figure 17.14: Tail of the internal conversion distri-bution overlaid with signal at different branchingratios for the phase II detector. The resolutionfor the internal conversion decays was taken from30 000 simulated signal decays.

three Michel decays 3×(µ → eνν) and from co-incidences of a radiative muon decay with in-ternal conversion µ → eee with a Michel decayµ → eνν. Both types of backgrounds are sig-nificantly reduced by applying vertex and timerequirements. The combinatorial Michel back-ground depends quadratically on the vertex andtime resolution, whereas the coincidences µ → eee× µ → eνν coincidence rate scale linearly with thevertex and the time resolution.

The vertex resolution in the transverse directioncan be represented by the distance of closest ap-proach when the track is extrapolated to the muondecay position. This values is about 185 µm in allphases of the experiment and given in Table 17.2.For a target size of 10 cm in length and 2 cm indiameter a reduction factor of 1 · 10−4 can be de-rived per coincidence.

The estimation of the reduction factor from thetiming cut, relevant for phases Ib and II, is difficultas the design for the time of flight system has notbeen finalised yet. Another difficulty comes fromthe fact that the timing resolutions of the scintil-lating fibre detector the scintillating tiles detector

are expected to be different and that particles de-pending on their flight direction will be measuredin both detectors or by the scintillating fibre de-tector only if staying in the central region. In thelatter case the particles will be measured manytimes in several turns, what also leads to an in-crease in precision. Preliminary studies indicatethat timing resolutions of 200-300 ps in the scin-tillating fibre detector and < 100 ps in the Scin-tillating Tiles Detector can be achieved, see sec-tions 11 and 12. For the sensitivity calculationit is assumed that all particles will be measuredwith a time resolution of better than 250 ps andthat reduction factors of 5 · 10−3 per coincidencecan be obtained at a signal efficiency of 90 %.

17.4 Results

The signal efficiencies and the expected back-ground reduction factors of the different selectioncuts are summarized in Table 17.3. Single eventsensitivities are calculated, which are defined asthe branching ratio at which one background eventis expected. The sensitivity of the experimentscales with one over the number of muons on tar-get as long as the single event sensitivity is notreached and with one over the square root of thenumber of muons on target after. It can be seenthat the single event sensitivity at phase IB ishigher than at phase II. This comes from the factthat the combinatorial background increases athigher muon rates. However, the time to reachthe aimed sensitivity of 1 · 10−16 takes in phase IBten years of running whereas at phase II this sens-itivity can be reached in 180 days because of thehigher muon rate, see Figure 17.15. Although theexpected sensitivity at phase IA, even without thetime of flight system, is quite high with 4 · 10−16

it would take a long time of running to reach thissensitivity. However, about one month of run-ning is sufficient to reach a sensitivity of 1 · 10−13,which is factor ten smaller than the current exper-imental bound.

89



Backgrounds:Michel 0 < 2.5 · 10−18 5 · 10−18

µ → eeeνν 1 · 10−16 1 · 10−17 1 · 10−17

µ → eeeνν and accidental Michel 0 < 2.5 · 10−21 7.5 · 10−18

Total Background 1 · 10−16 1 · 10−17 2.3 · 10−17

Signal:Track reconstruction and selection efficiency 26 % 39 % 38 %Kinematic cut (2σ) 95 % 95 % 95 %Vertex efficiency (2.5σ)2 98 % 98 % 98 %Timing efficiency (2σ)2 - 90 % 90 %Total efficiency 24 % 33 % 32 %

Sensitivity:Single event sensitivity 4 · 10−16 3 · 10−17 7 · 10−17

muons on target rate (Hz) 2 · 107 1 · 108 2 · 109

running days to reach 1 · 10−15 2600 350 18running days to reach 1 · 10−16 - 3500 180running days to reach single event sensitivity 6500 11 700 260

Table 17.3: Signal efficiencies and estimated background reduction factors of the discussed selection cuts,which are used to determine the single event sensitivities for the three phases of the experiment. For thegiven muon on target rates running times are calculated to reach the given single event sensitivities.

Figure 17.15: Projected sensitivity and projected limit (90% CL) of the Mu3e experiment for the threeconstruction phases IA (red), IB (magenta) and II (blue) as function of the running time. The curveswere obtained from the corresponding numbers in Table 17.3. For comparison also the (90% CL) obtainedfrom the SINDRUM experiment is indicated (black dashed line).

90

Part III

The Mu3e Collaboration

91

Chapter 18

The Institutes in Mu3e

18.1 Responsibilities

The responsibilities of the institutes participatingin Mu3e are outlined in Table 18.1. This list con-cerns the phase I experiment and does not implyfunding responsibilities.

18.2 Collaborators

18.2.1 University of Geneva

Currently working on Mu3e:Alain Blondel ProfessorAlessandro Bravar ProfessorMartin Pohl ProfessorAntoaneta Damyanova Master student

Planned positions:1 Postdoc1 Ph.D. candidate

18.2.2 University of Zürich

Currently working on Mu3e:Ueli Straumann ProfessorPeter Robmann Senior scientistRoman Gredig Ph.D. candidate

18.2.3 Paul Scherrer Institut

Currently working on Mu3e:Felix Berg Ph.D. candidateMalte Hildebrandt Senior scientistPeter-Raymond Kettle Senior scientistAngela Papa Senior scientist

Stefan Ritt Senior scientistAlexey Stoykov Senior scientistFunded open positions:1 Postdoc1 Ph.D. candidate

18.2.4 ETH Zürich

Currently working on Mu3e:Christophorus Grab ProfessorGünther Dissertori ProfessorRainer Wallny ProfessorPlanned positions:1 Ph.D. candidate

18.2.5 University of Heidelberg

Physikalisches Institut (PI)

Currently working on Mu3e:André Schöning ProfessorDirk Wiedner Senior scientistSebastian Bachmann Senior scientistNiklaus Berger Junior research group leaderBernd Windelband Mechanical engineerMoritz Kiehn Ph.D. candidateKevin Stumpf Mechanical engineerRaphael Philipp Master studentFunded open positions:1 Postdoc4 Ph.D. candidatesPlanned positions:1 Postdoc1 Ph.D. candidate

92


Kirchhoff Institut für Physik (KIP)

Currently working on Mu3e:Hans-Christian Schultz-Coulon ProfessorWei Shen PostdocPatrick Eckert Ph.D. candidateCarlo Licciulli Master studentTobias Hartwig Bachelor studentPlanned positions:1 Postdoc1 Ph.D. candidate

Zentralinstitut für Technische Informatik

Currently working on Mu3e:Peter Fischer ProfessorIvan Péric Senior scientist

Component Responsible

Beam PSI

Magnet UGSHeidelberg PI

Target Heidelberg PIPSI

Pixel chip ZITI MannheimHeidelberg PIHeidelberg NB

Pixel detector Heidelberg PI

Mechanics and cooling Heidelberg PI

Pixel on-detector electronics Heidelberg NBHeidelberg PI

Read-out electronics Heidelberg NB

Fibre detector GenevaZürichETHZPSI

Tile detector Heidelberg KIP

Timing electronics PSIHeidelberg KIPGenevaZürichETHZ

Filter farm Heidelberg NB

Slow control PSI

Infrastructure PSI

Table 18.1: Institutional interests and responsib-ilities in phase I Mu3e. NB denotes the EmmyNoether junior reserch group at the PhysikalischesInstitut led by N. Berger. UGS is an external en-gineering consultancy tasked with magnet designand procurement. Note that especially for largecommon items such as the magnet, design andconstruction responisbility does not imply fund-ing responsibility.

93

Chapter 19

Schedule

19.1 Phase I Schedule

Our goal is to take first data in 2015, with a pixel-only detector. Correspondingly, the timing crit-ical items are the central pixel detectors and themagnet. Prototyping on the first is well underwayand a first instrumented assembly correspondingto the vertex layers should be operational by late2013. Magnet design has also started, however thetendering process will consume about half a year;we hope the actual magnet construction will beunder way early in 2014.

For a second, longer run in 2016, we plan to in-tegrate the fibre detector as well as the inner recurlstations complete with timing tiles. As the outerrecurl stations are identical to the inner ones, we

plan to maintain the production capacities andmanufacture them during 2016.

Depending on the outcome of the 2016 run andthe schedule for the high intensity beam line, 2017could either be spend for phase II preparations orwith an extended run at the existing beamline.

19.2 Phase II Schedule

The phase II schedule is contingent on the sched-ule for the high intensity beamline. By 2017, wecan have all required detector components ready.If the phase I experience shows that major parts ofthe detector will have to be rebuilt, earliest phaseII startup would slip to 2018.

94

Chapter 20

Cost Estimates

Item Estimated cost(KCHF)

Beam line < 50Target < 10Pixel detector (central) 400Pixel detector (2 recurl stations) 200Scintillating fibres 200Tile detector (2 stations) 110Mechanics and cooling 200DAQ pixel detector 50DAQ fibres 200DAQ tiles 190Central DAQ 100Filter farm 50Slow control 50Infrastructure 100

Total 1910

Table 20.1: Estimated costs of the phase I experi-ment. The magnet (estimated at 500 KCHF) willbe loaned to Mu3e by PI Heidelberg for the runtime of the experiment.

Item Estimated cost(KCHF)

Beam line u.a.Target < 10Pixel detector (upgrade central) 200Pixel detector (2 recurl stations) 200Scintillating fibres 200Tile detector (2 stations) 110Mechanics and cooling 100DAQ pixel detector 50DAQ fibres 200DAQ tiles 190Central DAQ 100Filter farm 50Slow control 50Infrastructure u.a.

Total 1460

Table 20.2: Estimated costs of the phase II experi-ment. Items marked u.a. are under assesment; thenew beam line required will be by far the most ex-pensive item but also benefit many other users.

95

Chapter A

Appendix

A.1 Mu3e theses

Several theses involving the Mu3e project havebeen completed:

• M. Kiehn, diploma thesis Track Fitting withBroken Lines for the Mu3e Experiment,Heidelberg University, 2012.

• M. Zimmermann, bachelor thesis Coolingwith Gaseous Helium for the Mu3e Experi-ment, Heidelberg University, 2012.

• H. Augustin, bachelor thesis Charakterisier-ung von HV-MAPS, Heidelberg University,2012.

• A.-K. Perrevoort, master thesis Characterisa-tion of High Voltage Monolithic Active PixelSensors for the Mu3e Experiment, HeidelbergUniversity, 2012.

These theses are available in port-able document format (PDF) fromhttp://www.psi.ch/mu3e/documents. Sev-eral more theses are ongoing (thus titles arepreliminary):

• R. Gredig, doctoral thesis Fibre Trackerfor the Mu3e Experiment, Zürich University,started 2012.

• M. Kiehn, doctoral thesis Track Reconstruc-tion for the Mu3e Experiment, HeidelbergUniversity, started 2012.

• A. Damyanova, master thesis Fibre and SiPMcharacterization for the Mu3e Experiment,Geneva University, started 2012.

• R. Philipp, master thesis Tests of HighVoltage Monolithic Active Pixel Sensors forthe Mu3e Experiment, Heidelberg University,started 2012.

A.2 Acknowledgements

N. Berger would like to thank the DeutscheForschungsgemeinschaft (DFG) for funding hiswork on the Mu3e experiment through the EmmyNoether program and thus supporting the exper-iment at a crucial early stage.

M. Kiehn acknowledges support by the Interna-tional Max Planck Research School for PrecisionTests of Fundamental Symmetries.

96

Bibliography

[1] Y. Fukuda et al., [Super-Kamiokande Collabor-ation], “Evidence for oscillation of atmosphericneutrinos”, Phys. Rev. Lett., 81 1562–1567,1998, (arXiv:hep-ex/9807003).

[2] Q. R. Ahmad et al., [SNO Collaboration],“Measurement of the charged current interac-tions produced by B-8 solar neutrinos at the Sud-bury Neutrino Observatory”, Phys. Rev. Lett.,87 071301, 2001, (arXiv:nucl-ex/0106015).

[3] K. Eguchi et al., [KamLAND Collabora-tion], “First results from KamLAND: Evid-ence for reactor antineutrino disappear-ance”, Phys. Rev. Lett., 90 021802, 2003,(arXiv:hep-ex/0212021).

[4] J. C. Pati and A. Salam, “Lepton Number as theFourth Color”, Phys. Rev., D10 275–289, 1974.

[5] H. Georgi and S. L. Glashow, “Unity of All Ele-mentary Particle Forces”, Phys. Rev. Lett., 32

438–441, 1974.

[6] P. Langacker, “Grand Unified Theories and Pro-ton Decay”, Phys.Rep., 72 185, 1981.

[7] H. E. Haber and G. L. Kane, “The Search forSupersymmetry: Probing Physics Beyond theStandard Model”, Phys. Rept., 117 75, 1985.

[8] R. N. Mohapatra and J. C. Pati, “Left-RightGauge Symmetry and an Isoconjugate Model ofCP Violation”, Phys. Rev., D11 566–571, 1975.

[9] R. N. Mohapatra and J. C. Pati, “A NaturalLeft-Right Symmetry”, Phys. Rev., D11 2558,1975.

[10] G. Senjanovic and R. N. Mohapatra, “ExactLeft-Right Symmetry and Spontaneous Violationof Parity”, Phys. Rev., D12 1502, 1975.

[11] M. Kakizaki, Y. Ogura and F. Shima,“Lepton flavor violation in the triplet Higgsmodel”, Phys.Lett., B566 210–216, 2003,(arXiv:hep-ph/0304254).

[12] C. T. Hill and E. H. Simmons, “Strongdynamics and electroweak symmetry break-ing”, Phys. Rept., 381 235–402, 2003,(arXiv:hep-ph/0203079).

[13] M. L. Brooks et al., [MEGA Collabora-tion], “New limit for the family-number non-conserving decay µ+ → e+γ”, Phys. Rev. Lett.,83 1521–1524, 1999, (arXiv:hep-ex/9905013).

[14] J. Adam et al., [MEG Collaboration], “Newlimit on the lepton-flavour violating decay mu-> e gamma”, Phys. Rev. Lett., 107 171801,2011, (arXiv:1107.5547 [hep-ex]).

[15] U. Bellgardt et al., [SINDRUM Collabora-tion], “Search for the Decay µ+ → e+e+e−”,Nucl.Phys., B299 1, 1988.

[16] W. Bertl et al., [SINDRUM II Collaboration],“A Search for µ−e conversion in muonic gold”,Eur. Phys. J., C47 337–346, 2006.

[17] L. Calibbi, A. Faccia, A. Masiero andS.K. Vempati, “Lepton flavour violationfrom SUSY-GUTs: Where do we stand forMEG, PRISM/PRIME and a super flavourfactory”, Phys.Rev., D74 116002, 2006,(arXiv:hep-ph/0605139).

[18] S. Antusch, E. Arganda, M.J. Herrero and A.M.Teixeira, “Impact of theta(13) on lepton flavourviolating processes within SUSY seesaw”, JHEP,0611 090, 2006, (arXiv:hep-ph/0607263).

[19] F.P. An et al., [Daya Bay Collaboration],“Improved Measurement of Electron Antineut-rino Disappearance at Daya Bay”, 2012,(arXiv:1210.6327 [hep-ex]).

[20] J.K. Ahn et al., [RENO collaboration],“Observation of Reactor Electron Antineut-rino Disappearance in the RENO Experi-ment”, Phys.Rev.Lett., 108 191802, 2012,(arXiv:1204.0626 [hep-ex]).

[21] Y. Abe et al., [Double Chooz Collaboration],“Reactor electron antineutrino disappearance inthe Double Chooz experiment”, Phys.Rev., D86

052008, 2012, (arXiv:1207.6632 [hep-ex]).

97


[22] K. Abe et al., [T2K Collaboration], “Indica-tion of Electron Neutrino Appearance from anAccelerator-produced Off-axis Muon NeutrinoBeam”, Phys. Rev. Lett., 107 041801, 2011,(arXiv:1106.2822 [hep-ex]).

[23] D. Nicolo, [MEG Collaboration], “The µ → eγ

experiment at PSI”, Nucl.Instrum.Meth., A503

287–289, 2003.

[24] J. Adam et al., [MEG Collaboration], “Alimit for the µ → eγ decay from the MEGexperiment”, Nucl.Phys., B834 1–12, 2010,(arXiv:0908.2594 [hep-ex]).

[25] K. Hayasaka, [Belle Collaboration], “Tau leptonphysics at Belle”, Journal of Physics: Confer-ence Series, 335(1) 012029, 2011.

[26] K. Hayasaka et al., [Belle Collaboration], “Newsearch for τ → µγ and τ → eγ de-cays at Belle”, Phys.Lett., B666 16–22, 2008,(arXiv:0705.0650 [hep-ex]).

[27] B. Aubert et al., [BABAR Collabora-tion], “Searches for Lepton Flavor Vi-olation in the Decays τ± → e±γ andτ± → µ±γ”, Phys.Rev.Lett., 104 021802,2010, (arXiv:0908.2381 [hep-ex]).

[28] J. P. Lees et al., [BaBar Collaboration], “Limitson tau Lepton-Flavor Violating Decays in threecharged leptons”, Phys. Rev., D81 111101, 2010,(arXiv:1002.4550 [hep-ex]).

[29] B. Aubert et al., [BaBar Collaboration],“Searches for Lepton Flavor Violation in theDecays τ → eγ and τ → µγ”, Phys. Rev.Lett., 104 021802, 2010, (arXiv:0908.2381

[hep-ex]).

[30] B. Aubert et al., [BaBar Collaboration], “Im-proved limits on lepton flavor violating tau de-cays to ℓφ, ℓρ, ℓK∗ and ℓK∗”, Phys. Rev.Lett., 103 021801, 2009, (arXiv:0904.0339

[hep-ex]).

[31] B. Aubert et al., [BaBar Collaboration], “Searchfor Lepton Flavour Violating Decays τ → ℓK0

S

with the BaBar Experiment”, Phys. Rev., D79

012004, 2009, (arXiv:0812.3804 [hep-ex]).

[32] B. Aubert et al., [BaBar Collaboration], “Searchfor Lepton Flavor Violating Decays τ± → ℓ±ω

(ℓ = e, µ)”, Phys. Rev. Lett., 100 071802, 2008,(arXiv:0711.0980 [hep-ex]).

[33] B. Aubert et al., [BaBar Collaboration], “Searchfor Lepton Flavor Violating Decays τ± →ℓ±π0, ℓ±η, ℓ±η′”, Phys. Rev. Lett., 98 061803,2007, (arXiv:hep-ex/0610067).

[34] K. Hayasaka et al., [Belle Collaboration],“Search for Lepton Flavor Violating τ Decays

into Three Leptons with 719 Million Producedτ+τ− Pairs”, Phys. Lett., B687 139–143, 2010,(arXiv:1001.3221 [hep-ex]).

[35] Y. Miyazaki et al., [Belle Collaboration],“Search for Lepton Flavor Violating τ− Decaysinto ℓ−K0

s and ℓ−K0s K0

s ”, Phys. Lett., B692 4–9, 2010, (arXiv:1003.1183 [hep-ex]).

[36] Y. Miyazaki et al., [Belle Collaboration],“Search for Lepton Flavor and Lepton NumberViolating tau Decays into a Lepton and TwoCharged Mesons”, Phys. Lett., B682 355–362,2010, (arXiv:0908.3156 [hep-ex]).

[37] Y. Miyazaki et al., [Belle Collaboration],“Search for Lepton-Flavor-Violating tau De-cays into Lepton and f0(980) Meson”, Phys.Lett., B672 317–322, 2009, (arXiv:0810.3519

[hep-ex]).

[38] Y. Miyazaki et al., [Belle Collaboration],“Search for Lepton Flavor Violating tau Decaysinto Three Leptons”, Phys. Lett., B660 154–160, 2008, (arXiv:0711.2189 [hep-ex]).

[39] Y. Nishio et al., [Belle Collaboration], “Searchfor lepton-flavor-violating τ → ℓV 0 decaysat Belle”, Phys. Lett., B664 35–40, 2008,(arXiv:0801.2475 [hep-ex]).

[40] Y. Miyazaki et al., [Belle Collaboration],“Search for lepton flavor violating τ− decaysinto ℓ−η, ℓ−η′ and ℓ−π0”, Phys. Lett., B648

341–350, 2007, (arXiv:hep-ex/0703009).

[41] Y. Miyazaki et al., [Belle Collaboration],“Search for lepton flavor violating tau- decayswith a K0

S meson”, Phys. Lett., B639 159–164,2006, (arXiv:hep-ex/0605025).

[42] T. Aushev, W. Bartel, A. Bondar, J. Brodzicka,T.E. Browder et al., “Physics at Super B Fact-ory”, 2010, (arXiv:1002.5012 [hep-ex]).

[43] T. Abe, [Belle II Collaboration], “Belle II Tech-nical Design Report”, 2010, (arXiv:1011.0352

[physics.ins-det]).

[44] M. Aoki, [DeeMe Collaboration], “An experi-mental search for muon-electron conversion innuclear field at sensitivity of 10−14 with a pulsedproton beam”, AIP Conf.Proc., 1441 599–601,2012.

[45] R. Akhmetshin et al., [COMET Collabora-tion], “Experimental Proposal for Phase-I ofthe COMET Experiment at J-PARC”, KEK/J-PARC-PAC 2012-10, 2012.

[46] L. Bartoszek et al., [Mu2e Collabora-tion], “Mu2e Conceptual Design Report”,Fermilab-TM-2545, 2012, (arXiv:1211.7019

[physics.ins-det]).

98


[47] D.N. Brown, [Mu2e Collaboration], “Mu2e, acoherent mu → e conversion experiment at Fer-milab”, AIP Conf.Proc., 1441 596–598, 2012.

[48] L. Randall and R. Sundrum, “A large mass hier-archy from a small extra dimension”, Phys. Rev.Lett., 83 3370, 1999.

[49] N. Arkani-Hamed and M. Schmaltz, “Hierarch-ies without symmetries from extra dimensions”,Phys. Rev., D61 33005, 2000.

[50] Y. Kuno and Y. Okada, “Muon decayand physics beyond the standard model”,Rev. Mod. Phys., 73 151–202, 2001,(arXiv:hep-ph/9909265).

[51] J. Hisano, T. Moroi, K. Tobe and MasahiroYamaguchi, “Lepton flavor violation via right-handed neutrino Yukawa couplings in supersym-metric standard model”, Phys.Rev., D53 2442–2459, 1996, (arXiv:hep-ph/9510309).

[52] A. de Gouvêa, “(Charged) Lepton Flavor Viol-ation”, Nucl. Phys B. (Proc. Suppl.), 188 303–308, 2009.

[53] F. del Aguila, J.I. Illana and M.D. Jen-kins, “Precise limits from lepton flavour vi-olating processes on the Littlest Higgs modelwith T-parity”, JHEP, 0901 080, 2009,(arXiv:0811.2891 [hep-ph]).

[54] F. del Aguila, J. I. Illana and M. D. Jen-kins, “Lepton flavor violation in the SimplestLittle Higgs model”, JHEP, 1103 080, 2011,(arXiv:1101.2936 [hep-ph]).

[55] E. Arganda and M. J. Herrero, “Testing su-persymmetry with lepton flavor violating tauand mu decays”, Phys.Rev., D73 055003, 2006,(arXiv:hep-ph/0510405).

[56] M. Hirsch, F. Staub and A. Vicente, “Enhancingli → 3lj with the Z0-penguin”, Phys.Rev., D85

113013, 2012, (arXiv:1202.1825 [hep-ph]).

[57] H.K. Dreiner, K. Nickel, F. Staub andA. Vicente, “New bounds on trilinear R-parity violation from lepton flavor violatingobservables”, Phys.Rev., D86 015003, 2012,(arXiv:1204.5925 [hep-ph]).

[58] A. Abada, D. Das, A. Vicente and C. Weiland,“Enhancing lepton flavour violation in thesupersymmetric inverse seesaw beyond thedipole contribution”, JHEP, 1209 015, 2012,(arXiv:1206.6497 [hep-ph, reportNumber =

LPT-ORSAY-12-36]).

[59] M. Hirsch, W. Porod, L. Reichert and F. Staub,“Phenomenology of the minimal supersymmet-ric U(1)B−L × U(1)R extension of the stand-ard model”, Phys.Rev., D86 093018, 2012,(arXiv:1206.3516 [hep-ph]).

[60] G. Aad et al., [ATLAS Collaboration], “Searchfor pair-produced massive coloured scalars infour-jet final states with the ATLAS detectorin proton-proton collisions at sqrt(s) = 7 TeV”,2012, (arXiv:1210.4826 [hep-ex]).

[61] G. Aad et al., [ATLAS Collaboration], “Searchfor pair production of massive particles decayinginto three quarks with the ATLAS detector insqrt(s) = 7 TeV pp collisions at the LHC”, 2012,(arXiv:1210.4813 [hep-ex]).

[62] G. Aad et al., [ATLAS Collaboration], “Searchfor R-parity-violating supersymmetry in eventswith four or more leptons in sqrt(s) = 7 TeVpp collisions with the ATLAS detector”, 2012,(arXiv:1210.4457 [hep-ex]).

[63] G. Aad et al., [ATLAS Collaboration], “Searchfor direct chargino production in anomaly-mediated supersymmetry breaking models basedon a disappearing-track signature in pp colli-sions at sqrt(s)=7 TeV with the ATLAS de-tector”, 2012, (arXiv:1210.2852 [hep-ex]).

[64] G. Aad et al., [The ATLAS Collaboration],“Search for Supersymmetry in Events with LargeMissing Transverse Momentum, Jets, and atLeast One Tau Lepton in 7 TeV Proton-ProtonCollision Data with the ATLAS Detector”, 2012,(arXiv:1210.1314 [hep-ex]).

[65] G. Aad et al., [ATLAS Collaboration], “Searchfor a heavy top-quark partner in final stateswith two leptons with the ATLAS detector at theLHC”, 2012, (arXiv:1209.4186 [hep-ex]).

[66] G. Aad et al., [ATLAS Collaboration], “Searchfor light top squark pair production in final stateswith leptons and b-jets with the ATLAS detectorin sqrt(s) = 7 TeV proton-proton collisions”,2012, (arXiv:1209.2102 [hep-ex]).

[67] G. Aad et al., [ATLAS Collaboration], “Searchfor diphoton events with large missing trans-verse momentum in 7 TeV proton-proton col-lision data with the ATLAS detector”, 2012,(arXiv:1209.0753 [hep-ex]).

[68] G. Aad et al., [ATLAS Collaboration], “Furthersearch for supersymmetry at sqrt(s) = 7 TeVin final states with jets, missing transverse mo-mentum and isolated leptons with the ATLASdetector”, 2012, (arXiv:1208.4688 [hep-ex]).

[69] G. Aad et al., [ATLAS Collaboration], “Searchfor light scalar top quark pair production in fi-nal states with two leptons with the ATLAS de-tector in sqrt(s) = 7 TeV proton-proton colli-sions”, 2012, (arXiv:1208.4305 [hep-ex]).

99


[70] G. Aad et al., [ATLAS Collaboration], “Searchfor direct production of charginos and neut-ralinos in events with three leptons and miss-ing transverse momentum in sqrt(s) = 7 TeVpp collisions with the ATLAS detector”, 2012,(arXiv:1208.3144 [hep-ex]).

[71] G. Aad et al., [ATLAS Collaboration], “Searchfor direct slepton and gaugino production in fi-nal states with two leptons and missing trans-verse momentum with the ATLAS detectorin pp collisions at sqrt(s) = 7 TeV”, 2012,(arXiv:1208.2884 [hep-ex]).

[72] G. Aad et al., [ATLAS Collaboration], “Searchfor direct top squark pair production in finalstates with one isolated lepton, jets, and miss-ing transverse momentum in sqrt(s) = 7 TeV ppcollisions using 4.7 fb-1 of ATLAS data”, 2012,(arXiv:1208.2590 [hep-ex]).

[73] G. Aad et al., [ATLAS Collaboration], “Searchfor squarks and gluinos with the ATLAS de-tector in final states with jets and missingtransverse momentum using 4.7 fb−1 of sqrt(s)= 7 TeV proton-proton collision data”, 2012,(arXiv:1208.0949 [hep-ex]).

[74] G. Aad et al., [ATLAS Collaboration], “Searchfor top and bottom squarks from gluino pair pro-duction in final states with missing transverseenergy and at least three b-jets with the ATLASdetector”, 2012, (arXiv:1207.4686 [hep-ex]).

[75] G. Aad et al., [ATLAS Collaboration], “Huntfor new phenomena using large jet multiplicit-ies and missing transverse momentum with AT-LAS in 4.7 fb−1 of sqrt(s) = 7 TeV proton-proton collisions”, JHEP, 1207 167, 2012,(arXiv:1206.1760 [hep-ex]).

[76] S. Chatrchyan et al., [CMS Collaboration],“Search for supersymmetry in events withphotons and low missing transverse energyin pp collisions at sqrt(s) = 7 TeV”, 2012,(arXiv:1210.2052 [hep-ex]).

[77] S. Chatrchyan et al., [CMS Collaboration],“Search for electroweak production of chargi-nos and neutralinos using leptonic final statesin pp collisions at sqrt(s) = 7 TeV”, 2012,(arXiv:1209.6620 [hep-ex]).

[78] S. Chatrchyan et al., [CMS Collaboration],“Search for supersymmetry in hadronic fi-nal states using MT2 in pp collisions at√

s = 7 TeV”, JHEP, 1210 018, 2012,(arXiv:1207.1798 [hep-ex]).

[79] S. Chatrchyan et al., [CMS Collaboration],“Search for new physics in the multijet andmissing transverse momentum final state in

proton-proton collisions at√

s = 7 TeV”, 2012,(arXiv:1207.1898 [hep-ex]).

[80] S. Chatrchyan et al., [CMS Collaboration],“Search for new physics in events with opposite-sign leptons, jets, and missing transverse en-ergy in pp collisions at sqrt(s) = 7 TeV”, 2012,(arXiv:1206.3949 [hep-ex]).

[81] S. Chatrchyan et al., [CMS Collaboration],“Search for new physics with same-sign isolateddilepton events with jets and missing transverseenergy”, Phys.Rev.Lett., 109 071803, 2012,(arXiv:1205.6615 [hep-ex]).

[82] S. Chatrchyan et al., [CMS Collaboration],“Search for new physics in events with same-sign dileptons and b-tagged jets in pp collisionsat sqrt(s) = 7 TeV”, JHEP, 1208 110, 2012,(arXiv:1205.3933 [hep-ex]).

[83] S. Chatrchyan et al., [CMS Collaboration],“Search for anomalous production of multileptonevents in pp collisions at sqrt(s)=7 TeV”, JHEP,1206 169, 2012, (arXiv:1204.5341 [hep-ex]).

[84] S. Chatrchyan et al., [CMS Collaboration],“Search for physics beyond the standard modelin events with a Z boson, jets, and missingtransverse energy in pp collisions at sqrt(s)= 7 TeV”, Phys.Lett., B716 260–284, 2012,(arXiv:1204.3774 [hep-ex]).

[85] R.N. Mohapatra and J.W.F. Valle, “NeutrinoMass and Baryon Number Nonconservation inSuperstring Models”, Phys.Rev., D34 1642,1986.

[86] M. Malinsky, J.C. Romao and J.W.F. Valle,“Novel supersymmetric SO(10) seesaw mech-anism”, Phys.Rev.Lett., 95 161801, 2005,(arXiv:hep-ph/0506296).

[87] V. De Romeri, M. Hirsch and M. Malinsky, “Softmasses in SUSY SO(10) GUTs with low inter-mediate scales”, Phys.Rev., D84 053012, 2011,(arXiv:1107.3412 [hep-ph]).

[88] M. Blanke, A. J. Buras, B. Duling, A. Poschen-rieder and C. Tarantino, “Charged Lepton Fla-vour Violation and (g-2)(mu) in the LittlestHiggs Model with T-Parity: A Clear Distinctionfrom Supersymmetry”, JHEP, 0705 013, 2007,(arXiv:hep-ph/0702136).

[89] M. Blanke, A. J. Buras, B. Duling, S. Reck-siegel and C Tarantino, “FCNC Processes inthe Littlest Higgs Model with T-Parity: a 2009Look”, Acta Phys. Polon., B41 657–683, 2010,(arXiv:0906.5454 [hep-ph]).

[90] W.F. Chang and J. N. Ng, “Lepton flavor vi-olation in extra dimension models”, Phys.Rev.,D71 053003, 2005, (arXiv:hep-ph/0501161).

100


[91] S. Casagrande, F. Goertz, U. Haisch,M. Neubert and T. Pfoh, “Flavor Physicsin the Randall-Sundrum Model: I. TheoreticalSetup and Electroweak Precision Tests”, JHEP,10 094, 2008, (arXiv:0807.4937 [hep-ph]).

[92] M. S. Carena, A. Delgado, E. Ponton, T. M. P.Tait and C. E. M. Wagner, “Precision elec-troweak data and unification of couplings inwarped extra dimensions”, Phys. Rev., D68

035010, 2003, (arXiv:hep-ph/0305188).

[93] A. Delgado and A. Falkowski, “Electroweak ob-servables in a general 5D background”, JHEP,05 097, 2007, (arXiv:hep-ph/0702234).

[94] W. Bertl, SINDRUM I, Presentation at PSI,2008.

[95] Y. Amhis et al., [Heavy Flavor AveragingGroup], “Averages of b-hadron, c-hadron, andtau-lepton properties as of early 2012”, 2012,(arXiv:1207.1158 [hep-ex]).

[96] M. Bona et al., [SuperB Collaboration], “Su-perB: A High-Luminosity Asymmetric e+ e- Su-per Flavor Factory. Conceptual Design Report”,2007, (arXiv:0709.0451 [hep-ex]).

[97] J. Kaulard et al., [SINDRUM II Collaboration],“Improved limit on the branching ratio of µ− →e+ conversion on titanium”, Phys.Lett., B422

334–338, 1998.

[98] C. Dohmen et al., [SINDRUM II Collaboration],“Test of lepton flavor conservation in µ → e

conversion on titanium”, Phys. Lett., B317

631–636, 1993.

[99] R.M. Carey et al., [Mu2e Collaboration], “Pro-posal to search for µ−N → e−N with a singleevent sensitivity below 10−16”, 2008, Spokesper-sons: J.P. Miller, R.H. Bernstein.

[100] R. Tschirhart, “The Mu2e experiment at Ferm-ilab”, Nucl.Phys.Proc.Suppl., 210-211 245–248,2011.

[101] Y.G. Cui et al., [COMET Collaboration], “Con-ceptual design report for experimental searchfor lepton flavor violating mu- - e- conversionat sensitivity of 10−16 with a slow-extractedbunched proton beam (COMET)”, 2009.

[102] Y. Kuno, [COMET Collaboration], “Searchfor muon to electron conversion at J-PARC:COMET”, PoS, ICHEP2010 526, 2010.

[103] Y. Kuno, “Lepton flavor violation: Muonto electron conversion, COMET andPRISM/PRIME at J-PARC”, PoS, NU-

FACT08 111, 2008.

[104] J. Pasternak, L. Jenner, Y. Uchida, R. Barlow,K. Hock et al., “Accelerator and Particle Phys-ics Research for the Next Generation Muon to

Electron Conversion Experiment - the PRISMTask Force”, WEPE056, 2010.

[105] A. Yamamoto, M.Y. Yoshida, T. Ogitsu,Y. Mori, Y. Kuno et al., “MuSIC, the World’sHighest Intensity DC Muon Beam using a PionCapture System”, Conf.Proc., C110904 820–822, 2011.

[106] T. Ogitsu, A. Yamamoto, M.Y. Yoshida,Y. Kuno, H. Sakamoto et al., “A New Continu-ous Muon Beam Line Using a Highly EfficientPion Capture System at RCNP”, Conf.Proc.,C110328 856–858, 2011.

[107] The LHCb collaboration, Search for the leptonflavour violating decay τ− → µ+µ−µ−, InFlavor Physics and CP Violation 2012 (FPCP2012), 2012, LHCb-CONF-2012-015.

[108] P. Seyfert, “Searches for Lepton Flavour Viol-ation and Lepton Number Violation in HadronDecays”, 2012, (arXiv:1209.4939 [hep-ex]).

[109] R. Akers et al., [OPAL Collaboration], “ASearch for lepton flavor violating Z0 decays”,Z.Phys., C67 555–564, 1995.

[110] P. Abreu et al., [DELPHI Collaboration],“Search for lepton flavor number violating Z0

decays”, Z.Phys., C73 243–251, 1997.

[111] O. Adriani et al., [L3 Collaboration], “Search forlepton flavor violation in Z decays”, Phys.Lett.,B316 427–434, 1993.

[112] D. Decamp et al., [ALEPH Collaboration],“Searches for new particles in Z decays usingthe ALEPH detector”, Phys.Rept., 216 253–340, 1992.

[113] S. Davidson, S. Lacroix and P. Verdier, “LHCsensitivity to lepton flavour violating Z boson de-cays”, 2012, (arXiv:1207.4894 [hep-ph]).

[114] G. Aad et al., [ATLAS Collaboration], “Obser-vation of a new particle in the search for theStandard Model Higgs boson with the ATLASdetector at the LHC”, 2012, (arXiv:1207.7214

[hep-ex]).

[115] S. Chatrchyan et al., [CMS Collaboration],“Observation of a new boson at a mass of125 GeV with the CMS experiment at theLHC”, Phys.Lett.B, 2012, (arXiv:1207.7235

[hep-ex]).

[116] R. M. Djilkibaev and R. V. Konoplich, “RareMuon Decay µ+ → e+e−e+νeνµ”, Phys.Rev.,D79 073004, 2009, (arXiv:0812.1355

[hep-ph]).

[117] K. Nakamura et al., [Particle Data Group], “Re-view of particle physics”, J. Phys., G37 075021,2010.

101


[118] P.-R. Kettle, PSI-internal, LTP Filzbach Meet-ing, June 2010.

[119] A.E. Pifer, T. Bowen and K.R. Kend-all, “A High Stopping Density mu+ Beam”,Nucl.Instrum.Meth., 135 39–46, 1976.

[120] G.S. Bauer, Y. Dai and W. Wagner, “SINQ lay-out, operation, applications and R&D to highpower”, J. Phys. IV France, 12(8) 3–26, 2002.

[121] J. F. Crawford et al., “Production of low energypions by 590 MeV protons on nuclei”, HelveticaPhysica Acta, 53 497–505, 1980.

[122] J.F. Crawford et al., “Measurement of cross sec-tions and asymmetry parameters for the pro-duction of charged pions from various nuclei by585-MeV protons”, Phys. Rev. C, 22 1184–1196,1980.

[123] J. Brzezniak, R.W. Fast, Kurt J. Krempetz,A. Kristalinski, A. Lee et al., “Conceptualdesign of a 2-Tesla superconducting solenoidfor the Fermilab D0 detector upgrade”, 1994,FERMILAB-TM-1886.

[124] S. Agostinelli et al., “Geant4–a simulationtoolkit”, Nucl. Instr. Meth., A 506(3) 250 – 303,2003.

[125] W. Erdmann, W. Bertl, R. Horisberger,H.C. Kastli, D. Kotlinski et al., “Upgradeplans for the CMS pixel barrel detector”,Nucl.Instrum.Meth., A617 534–537, 2010.

[126] C. Grab, A Search for the Decay µ+ → e+e+e−,PhD thesis, Universität Zürich, 1985.

[127] I. Peric, “A novel monolithic pixelated particledetector implemented in high-voltage CMOStechnology”, Nucl.Instrum.Meth., A582 876–885, 2007.

[128] I. Peric and C. Takacs, “Large monolithicparticle pixel-detector in high-voltage CMOStechnology”, Nucl. Instrum. Meth., A624(2) 504– 508, 2010, New Developments in RadiationDetectors - ”Proceedings of the 11th EuropeanSymposium on Semiconductor Detectors, 11thEuropean Symposium on Semiconductor De-tectors”.

[129] I. Peric, C. Kreidl and P. Fischer, “Particlepixel detectors in high-voltage CMOS techno-logy - New achievements”, Nucl. Instr. Meth., A

650(1) 158 – 162, 2011, International Workshopon Semiconductor Pixel Detectors for Particlesand Imaging 2010.

[130] I. Peric, Private communication, 2010.

[131] IBM Corporation, IBM CMOS 7 HV, 2012,TGD03019USEN.

[132] Institute of Electrical and Electronics Engineers,IEEE 1149.1: Standard Test Access Port andBoundary Scan Architecture, 2001.

[133] A.-K. Perrevoort, Characterisation of High-Voltage MonolithicActive Pixel Sensors for theMu3e Experiment, Master’s thesis, HeidelbergUniversity, 2012.

[134] H. Augustin, Charakterisierung von HV-MAPS,Bachelor thesis, Heidelberg University, 2012.

[135] K. Akiba, M. Artuso, R. Badman, A. Borgia,R. Bates et al., “Charged Particle Tracking withthe Timepix ASIC”, Nucl.Instrum.Meth.,A661 31–49, 2012, (arXiv:1103.2739

[physics.ins-det]).

[136] M. Zimmermann, Cooling with Gaseous He-lium for the Mu3e Experiment, Bachelor thesis,Heidelberg University, 2012.

[137] G. Dellacasa et al., [ALICE Collaboration],“ALICE: Technical design report of the timeprojection chamber”, 2000.

[138] A. Boyarski, D. Briggs and P. Burchat,“Studies of helium based drift chamber gasesfor high luminosity low-energy machines”,Nucl.Instrum.Meth., A323 267–272, 1992.

[139] F. V. Böhmer, M. Ball, S. Dørheim, C. Höppner,B. Ketzer, I. Konorov, S. Neubert, S. Paul,J. Rauch and M. Vandenbroucke, “Space-ChargeEffects in an Ungated GEM-based TPC”, ArXive-prints, September 2012, (arXiv:1209.0482

[physics.ins-det]).

[140] S. Margetis, [STAR Collaboration], “Heavy Fla-vor Tracker (HFT): The new silicon vertexdetector for the STAR experiment at RHIC”,Nucl.Phys.Proc.Suppl., 210-211 227–230, 2011.

[141] I. Valin, C. Hu-Guo, J. Baudot, G. Bertolone,A. Besson et al., “A reticle size CMOS pixelsensor dedicated to the STAR HFT”, JINST, 7

C01102, 2012.

[142] L. Greiner, A MAPS based pixel vertex detectorfor the STAR experiment, In VERTEX, 2012.

[143] C. Kreidl, Belle tracker upgrade, In VERTEX,2012.

[144] M. van Beuzekom, VeloPix ASIC developmentfor the LHCb VELO upgrade, In PIXEL, 2012.

[145] P. Abbon et al., [COMPASS Collabora-tion], “The COMPASS experiment at CERN”,Nucl.Instrum.Meth., A577 455–518, 2007,(arXiv:hep-ex/0703049).

[146] B. Beischer et al., “A high-resolution scin-tillating fiber tracker with silicon photomul-tiplier array readout”, Nucl.Instrum.Meth.,A622 542–554, 2010, (arXiv:1011.0226

[physics.ins-det]).

102


[147] B. Beischer et al., “The development of a high-resolution scintillating fiber tracker with siliconphotomultiplier readout”, Nucl.Instrum.Meth.,A628 403–406, 2011.

[148] P. Eckert, R. Stamen and H.C. Schultz-Coulon,“Study of the response and photon-counting res-olution of silicon photomultipliers using a gen-eric simulation framework”, JINST, 7 P08011,2012, (arXiv:1206.4154 [physics.ins-det]).

[149] J.Y. Wu and Z.H. Shi, “The 10-ps wave unionTDC: Improving FPGA TDC resolution beyondits cell delay”, 2008.

[150] P. Pütsch, Transmission Line Evaluation andPrototype Test of the Data Handling ProcessorReadout Chip for the Belle II DEPFET PixelDetector, Master thesis, Bonn University, 2011.

[151] F Vasey, D Hall, T Huffman, S Kwan, A Prosser,C Soos, J Troska, T Weidberg, A Xiang andJ Ye, “The Versatile Link common project: feas-ibility report”, JINST, 7(01) C01075, 2012.

[152] J. Troska, Technical Specification VERSATILETRANSCEIVER (a.k.a CERN SFP+, VTRx,VTTx), CMS Document 4802-v2, 2012.

[153] S. Swientek, Upgrade der Backend-Ausleseelektronik für den LHCb Outer Tracker,In DPG Spring Meeting, 2012.

[154] G. Haefeli, A. Bay, A. Gong, H. Gong,M. Muecke et al., “The LHCb DAQ interfaceboard TELL1”, Nucl.Instrum.Meth., A560 494–502, 2006.

[155] Wolfgang Kühn et al., [PANDA Collabora-tion], “FPGA based compute nodes for high leveltriggering in PANDA”, J.Phys.Conf.Ser., 119

022027, 2008.

[156] K. Olchanski S. Ritt, P. Amaudruz, MaximumIntegration Data Acquisition System, 2001,http://midas.psi.ch.

[157] K. Abe et al., [T2K Collaboration], “TheT2K Experiment”, Nucl.Instrum.Meth.,A659 106–135, 2011, (arXiv:1106.1238

[physics.ins-det]).

[158] L.M. Brarkov et al., “Search for µ+ → e+γ downto 10−14 branching ratio”, Research Proposal toPSI, 1999.

[159] R. Schmidt S. Ritt, MSCB (MIDAS Slow Con-trol Bus), 2001, http://midas.psi.ch/mscb.

[160] EPICS (Experimental Physicsand Industrial Control System),http://www.aps.anl.gov/epics.

[161] Xilinx Coropration, VC707 Evaluation Boardfor the Virtex-7 FPGA - User Guide, 1.1 edi-tion, 2012.

[162] Altera Coropration, Stratix IV GX FPGA De-velopment Kit - User Guide, 9.1.0 edition, 2010.

[163] Altera Coropration, Stratix IV GX FPGA De-velopment Board - Refernce Manual, 9.1.0 edi-tion, 2012.

[164] D. Wiedner et al., Prototype IF14-1 for anOptical 12 input Receiver Card for the LHCbTELL1 Board, 2004, LHCb-2004-072.

[165] NVIDIA Corporation, NVIDIA GeForce GTX680, 2012, Whitepaper.

[166] AMD Corporation, AMD Graphics Cores Next(GCN) Architecture, 2012, Whitepaper.

[167] J. Allison, K. Amako, J. Apostolakis, H. Araujo,P.A. Dubois et al., “Geant4 developments andapplications”, IEEE Trans. Nucl. Sci., 53 270,2006.

[168] L. Urbán, A model for multiple scatteringin GEANT4. oai:cds.cern.ch:1004190, Tech-nical Report CERN-OPEN-2006-077, CERN,Geneva, Dec 2006.

[169] F. Scheck, “Muon Physics”, Phys.Rept., 44 187,1978.

[170] W.E. Fischer and F. Scheck, “Electron Polariz-ation in Polarized Muon Decay: Radiative Cor-rections”, Nucl.Phys., B83 25, 1974.

[171] P. Depommier and A. Vacheret, Radiative muondecay, Technical report, TWIST Technote No55, 2001.

[172] C. Fronsdal and H. Uberall, “mu-Meson De-cay with Inner Bremsstrahlung”, Phys.Rev., 113

654–657, 1959.

[173] R. Kleiss, W.J. Stirling and S.D. Ellis, “A newMonte Carlo treatment of multiparticle phasespace at high energies”, Comp. Phys. Commun.,40 359 – 373, 1986.

[174] V. Karimäki, “Effective circle fitting for particletrajectories”, Nucl. Instr. and Meth., A305 187,1991.

[175] V. Blobel, C. Kleinwort and F. Meier,“Fast alignment of a complex tracking de-tector using advanced track models”, Com-put.Phys.Commun., 182 1760–1763, 2011,(arXiv:1103.3909 [physics.ins-det]).

[176] C. Kleinwort, “General Broken Linesas advanced track fitting method”, 2012,(arXiv:1201.4320 [physics.ins-det]).

[177] A. Schöning, A Fast 3-Dimensional TrackFit with Multiple Scattering, Talk given atthe Mu3e Collaboration meeting, Internalnote Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, October 2012.

103

[178] M. Kiehn, Track Fitting with Broken Lines forthe MU3E Experiment, Diploma thesis, Heidel-berg University, 2012.

[179] M. Kiehn, Track reconstruction for the Mu3e ex-periment, PhD thesis, Heidelberg University, In

preparation.

[180] A. Schöning, RECOPIX, A Fast Track Recon-strcution based on Multiple Scattering Fits,Talk given at the Mu3e Collaboration meeting,November 2012.

104

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