detection of z gauge bosons in the di-muon decay...

CMS Physics Meeting 1 R. Cousins, J. Mumford, June 10, 2004 S. Valuev

Detection of Z′ Gauge Bosons in the Di-muon Decay Mode

Robert Cousins, Jason Mumford and Slava Valuev

University of California, Los Angeles

CMS Physics Meeting June 10, 2004


Introduction• Z′ bosons appear in many models beyond SM.• Z′ → µ+µ− is on list to be studied extensively for Physics TDR:

– Detailed signal and background studies, with the use of most complex available tools (full simulation, full reconstruction, etc.).

– As close to reality as possible (background uncertainties, detector misalignment, calibration and B field uncertainties, etc.).

– Strategy for physics as a function of luminosity.

• Main Z′ physics goals:– Understand discovery potential and optimize the search strategy

• main observable: Mµ+µ−.– Work out algorithms to distinguish among models (incl. graviton) and

study properties, once discovered• main observables: AFB on- and off-peak, y, σ·Br, Γ.

This analysis

Work in progress


This analysis is discussed in more detail in:– Analysis note CMS AN 2004/002.– Talks at SUSY/BSM meetings, 10 December 2003 and 17 March 2004.– Talk at PRS meeting, 11 May 2004.

Talks on related subjects by UCLA group (see other references therein):– Status of a Study of High-Mass Muon Pairs from Drell-Yan and Z′ (PRS/µ meeting, 24

Sept. 2002; US-CMS physics meeting, 18 Oct. 2002).– A Look at Track Quality Variables Inside Kalman Filter Fits to Tracker and Muon Hits

(PRS/µ meeting, 18 Feb. 2003).– Status of Z' Background Study for Data Challenge 2004 (PRS/µ meeting, 1 April 2003).– Status of a Study of High-Mass Muon Pairs from Drell-Yan, Z', and Gravitons (SUSY/BSM

meeting, 7 May 2003).– Root-Based Muon Analysis - A Users Perspective (Analysis Micro-Workshop, 1 July 2003).– Progress in Fitting High-Momentum Muons in ORCA (PRS/µ and SUSY/BSM meetings,

16-17 Sept. 2003).– Modus Operandi for Z′ Analysis (EMU meeting, 10 January 2004).– Status of a Study of Simulated and Reconstructed Z′ Events in CMS (Workshop on Muons

at the LHC and Tevatron, 14 April 2004).

References


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Z′ → µ+µ−: signal and backgrounds• Z′s arise in many models:

– ZSSM in sequential standard model (benchmark toy model);

– Z′ = ZψcosθE6 + ZχsinθE6 in E6and/or SO(10) models:Zψ, Zχ and Zη (θE6 = 37.78o);

– ZLRM and ZALRM in left-right symmetric models;

– etc.

• Limits on the mass:– Current: 600-800 GeV;– Expected by LHC start-up: ≤ 1 TeV.

• Br(Z′ → µ+µ−): 2-8%(if no exotic decay channels are open)

PYTHIA cross-sections; no added K-factors

• Dominant (and irreducible) background: Drell-Yan production of muon pairs pp → γ/Z0 → µ+µ−.

• Other sources: ZZ, WZ, WW, tt-bar, bb-bar, etc.

(studied as part of setting up DC04)

3 TeV ZSSM

DY

tt di-bosons


Generation and reconstruction• Monte Carlo samples:

couplings from literature, generated with PYTHIA6.1– ZSSM, Zψ, Zη, Zχ, ZLRM, ZALRM at 1, 3 and 5 TeV decaying to µ+µ− (1000 events

each);– Drell-Yan µ+µ− pairs above 0.2, 0.4, 1, 1.5, 2 and 3 TeV (1000 events each).

• Simulation and reconstruction:CMSIM 125, ORCA_6_3_0 (no pile-up)

– apply L1 and HLT requirements (pT and η thresholds et al., except for isolation);

– use MuonAnalysis package as an analysis framework;– use L1-seeded Global Muon Reconstructor (GMR) for muon identification;– for off-line reconstruction, refit the GMR-found hits using an optimized

combination of tracker-plus-first-muon-station and tracker-only fits (Truncated Muon Reconstructor, TMR) → see three next slides.


• Tracker plus full muon system (“Global Muon Reconstructor”, GMR)– 5 Parameter measurement at inner surface of tracker from backward part of Kalman filter fit to tracker and muon hits

(default fitting method).– http://agenda.cern.ch/askArchive.php?base=agenda&categ=a03423&id=a03423s1t0/transparencies for more information.

• Tracker only – Use only tracker hits for Kalman filter. Take measurement from innermost tracker surface.– Available as reconstruction option in ORCA (implementation by N. Neumeister).

• Tracker plus first muon station– Use tracker and hits from first muon station which contains hits.

Some possible track fitting methods

Tracker System Muon System

Forward filterMeasure here

Use scaled final forward values to initialize backward filter

CSC, DTIronBackward filter




Optimization of high-pT muon track fitting• Different fitting methods offer certain features:

– GMR – current default for muons, uses all muon hits.– Tracker only – smallest pT-resolution tails, smallest RMS in barrel,

and (currently) best pulls.– Tracker plus first muon station – best fitted pT-resolution sigma of the

3 methods considered.• Fits can be compared to choose fit method track-by-track.

– Kalman filter variables can be used as criteria for replacing bad fits.– Currently use tracker-plus-first-muon-station fit, but replace it by

tracker-only fit if it has much better probability of χ2 given N degrees of freedom (about 10% of all tracks).

(“Truncated Muon Reconstructor”, TMR)

(See J. Mumford’s talks at PRS/µ meetings in February and September 2003 for more details.)


TMR has narrower signal, perhaps reduced background tails.

ORCA 6.3.0 Digis MuonAnalysis package

Note: Optimization algorithm wastuned on different sample.

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Mµ+ µ- (GeV)

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Event selection• Both µ+ and µ− should be within ׀η ׀ < 2.4 and pass the trigger:

– Acceptance efficiency: raises from about 80% at 1 TeV to more than 95% at very high Mµµ (Figure below);

– L1/HLT trigger efficiency: about 98% at 1 TeV, about 95% at 5 TeV.

• Require that there are at least two µ’s of opposite charge sign.• No background-rejection cuts.• Overall efficiency: 70-75% (1-5 TeV).


• Generate ensembles of MC experiments:– number of events in each experiment fluctuates according to Poisson

distribution with a mean of σ·Br·(∫Ldt)·ε;– appropriately add Drell-Yan contribution from lower masses.

• In each experiment, fit Mµµ values using an unbinned maximum likelihood:

– ps (signal pdf) is a convolution of a Breit-Wigner with a Gaussian smearing;– pb (background pdf) is an exponential, with the slope parameter determined

from fits to Drell-Yan events.

Up to three free parameters: signal fraction (Ns / Ntot), signal mean (m0), and signal FWHM (Γ).

No constraints on the absolute background level: fit assumes only background shape is known.

Fitting procedure

)(1),;()( µµ0µµµµ MpNNmMp

NNMp b

tot

ss

tot

s ⋅

−+Γ⋅=


(1 TeV: just above expectedCDF/D0 mass reach;

∫Ldt = 0.1 fb-1: a few days of LHC low-luminosity running)

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True (PYTHIA) mass

Example: Zψ at 1 TeV, ∫Ldt = 0.1 fb-1

“Non-fluctuating” mass spectra:(stat. much larger than expected)

generated and reconstructed

Z′

DY Z′DY

Realistic mass spectra:two typical MC experiments

SL = 3.6

σm = 3.9%

S+B fit

B-only fit

SL = 7.1


(Still have to account for the radiative tail in the mass distribution in the fits)

Entries 25

Mean 998.4

RMS 19.19

Underflow 1

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/ ndf 2χ 5.753 / 18

Prob 0.9971

Constant 0.252± 1.009

Mean 3.9± 998.4

Sigma 2.74± 18.98

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Entries 45

Mean 2956

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Underflow 0

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Prob 0.738

Constant 0.393± 2.154

Mean 12.4± 2955

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Prob 0.738

Constant 0.393± 2.154

Mean 12.4± 2955

Sigma 8.78± 83.36

-1, 5 fbSSM3 TeV Z

Fit results: m0 and Γ

• Signal Γ: hard to reconstruct (FWHM dominated by resolution smearing)

• Signal mean mass: close to true value, small spread. Measured with precision of 4% (at high masses and discovery limit) or better

1 TeV Zψ, ∫Ldt = 0.1 fb-1

Mean mass = 998 GeV; RMS = 19 GeV

3 TeV ZSSM, ∫Ldt = 5 fb-1

Mean mass = 2960 GeV; RMS = 80 GeV


Significance estimators (I)Discussed in detail in V. Bartsch and G. Quast, CMS IN 2003/039

• Use likelihood-ratio estimator SL to calculate significance of an observed “signal”:

where– LS+B is the maximum likelihood from the signal-plus-background fit (p),– LB is the maximum likelihood from the background-only fit (pb).

Justification: • In the large-statistics limit, SL

2 is expected to follow a χ2-distribution with ndof equal to the difference in the number of free parameters between S+B and B-only hypotheses (theorem proved by S.S. Wilks in 1938).

• If ndof is one, then distribution of SL is a standard Gaussian.• Therefore, SL gives the probability (expressed in number of σ’s) that the pure

background fakes a signal (i.e. significance).

,)ln(2 BBSL LLS +=


Significance estimators (II)• For comparison with SL, also try a few other commonly used

(“counting”) estimators:

• Usual convention: S > 5 is necessary to establish a discovery(probability of 2.9·10-7 that the pure background would mimic a signal)

),(2

,

,

12c

2c

1c

BBS

BSS

BS

NNNS

NNNS

NNS

−+×=

+=

=

(proposed by S. Bityukov and N. Krasnikov)

( ) ( )( ).exp1ln2c SNN

BSL NNNS BS −+= +

NS and NB − number of signal and background events within m0 ± 2σ.


Significance estimators: MC studyImportant caveat: Wilks’ theorem is valid in the large-statistics limit, whereas we are in the small-statistics regime

Need to check that the tails of SL distribution for the background-only sample are those of the normal Gaussian

• Perform a (large) number of background-only MC experiments to obtain the distributions of various definitions of S given above.

• Calculate the probability (p-value) of observing a value of S greater than Scrit (how often a false discovery would be claimed for a certain choice of Scrit).

• See how well this probability agrees with area in the tail of a Gaussian distribution.


Background-only mass fits: significance

0 1 2 3 4 5 6 7 8 9 10

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Sc1 Sc1_recEntries 50

Mean 0.4156

RMS 0.5764Underflow 0

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Sc1 ScL_recEntries 1000000

Mean 0.3171


Overflow 0

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ScL ScL_recEntries 1000000

Mean 0.3171


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RMS 0.4704

Underflow 0

Overflow 0

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Mean 0.2997

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Mean 0.259

RMS 0.3892

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RMS 0.3892

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Mean 0.3627


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Mean 0.3627


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SL

Background to 3 TeV Z′ (30 fb-1)

too many events at large Sc1

Observed:SL > 3: 1310 eventsSL > 4: 38 eventsSL > 5: 1 events

BS NN1,000,000 MC experiments<Nevt> above 1.5 TeV: 33<Nevt> within m0 ± 2σm: 2.3

SL

ScL

Sc12 Sc2

Expected for a Gaussian:Above 3σ: 1350 eventsAbove 4σ: 31.5 eventsAbove 5σ: 0.3 events

Fix both m0 and Γ to true values(see Wilks’ theorem)


Significance estimators: MC studyCheck p-values for a few other integrated luminosities and signal mass points:• in these cases tail of SL distribution is always consistent with that of a

Gaussian;• all other S estimators may overestimate or underestimate the

probability of a false discovery.Also check distributions of S for signal-plus-background fits:• Sc1 >> SL, Sc12 ~ SL for all masses, luminosities, Z′ models;• SL is always symmetric and Gaussian-like.

Significance estimator SL performs as desired for Z′ mass reach studies (low background, small statistics regime).

Similarly good performance of SL was seen by Bartsch and Quast in H → 4µ studies, in a different sig/bknd regime.


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/ ndf 2χ 12.22 / 16Prob 0.7288Constant 0.1333± 0.5006 Mean 1.00± 12.25 Sigma 0.791± 4.613

Sc1

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SL

Zψ at 1 TeV, 0.1 fb-1: significance

• Sc1 >> SL

• Sc2 < SL

• Sc12 ≤ SL

(in agreement with other Z′ models,

masses, luminosities tried)

b

s

NN

bs

s

NNN

+)

(2

b

bs

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−

+×

LS

Fix both m0 and Γ to true values to calculate SL

LSc

• For 0.1 fb-1, average SL is more than 5 for all the Z′ models considered.

• TMR reconstruction of high-pT muons gives ~ 5% higher SL (15% at 3 TeV, 30% at 5 TeV).

• SL scales very nicely with .∫ Ldt


Z’ mass (TeV)1 2 3 4 5 6

)

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significance curvesσ: 5-µ +µ →Z’

ψZηZ

χZLRMZSSMZ

ALRMZ

significance curvesσ: 5-µ +µ →Z’

Z′→µ+µ−: CMS discovery potential

Z′ → µ+µ− mass reach:• > 1 TeV with 0.1 fb-1

• 2.7 − 3.6 TeV with 10 fb-1

• 3.7 − 4.7 TeV with 100 fb-1

N.B.: no syst. uncertainties• Perfect alignment,

calibration, B field;• Background shape,

functional forms of pdf’s, mass resolution perfectly known.

ORCA 6.3.0no pile-up

(if GMR is used, 100 GeV less with 10 fb-1

and 200 GeV less with 100 fb-1)


A critical look• Main weak point: systematic uncertainties are not taken into

account.– Arising from imperfect knowledge of the detector: alignment,

magnetic field, calibration, etc.– In the fitting procedure: background shape, functional forms of

pdf’s, mass resolution, etc.

• Some other items to be improved/checked:– Brem photons. Not used in the reconstruction of muon momentum;

residual radiative tail not accounted for in the fits.– Software. Set of PYTHIA, CMSIM and ORCA is 1.5 years old.– Event rates. Given by PYTHIA; need to check K-factors.– Pile-up. Neglected; effect is expected to be small, but not proven.

How does this study compare with the previous ones?


Previous studies of CMS discovery potential (I)Estimates of the CMS potential to discover Z′ were previously reported by four groups/individuals. In chronological order:– C.E. Wulz: (CMS-TN/93-107 and DPF/DPB Snowmass (1996))

• Tools: PYTHIA version available at that time; muon momentum smeared using parameterization by W. Ko and J. Rowe (CMS TN/95-026).

• Criterion for Z′ discovery: more than 10 signal (di-muon plus di-electron) events in the mass peak.

• Conclusion: it will be possible to discover Z′ bosons up to a mass of about 5 TeV with an integrated luminosity of 100 fb-1 (in a combined analysis of Z′ → µ+µ− and Z′ → e+e– channels).

– D. Bourilkov: (CMS IN-2000/035 and CERN-YR-2000-004)• Study mainly dedicated to Drell-Yan production of lepton pairs at LHC.• Tools: PYTHIA; no further details given.• Conclusion: “Z′ resonances with masses up to ~ 4-5 TeV can be probed at LHC”.


– JINR group (V. Palichik, S. Shmatov et al.):(hep-ph/0310336, talks at CMS physics (30 April 2002) and SUSY/BSM meetings (7 May 2003); presented at “Physics at LHC”, Prague 2003)

• Tools: PYTHIA; muon momentum smeared using parameterization by W. Ko and J. Rowe.

• Criterion for Z′ discovery: Sc1 > 5 and at least 10 signal events under the mass peak.

• Conclusions: Z′ mass reach is in the range between 2.5 and 3 TeV for an integrated luminosity of 10 fb-1, and between 3.5 and 4 TeV for a luminosity of 100 fb-1 (for a set of Z′ models similar to one we studied).

– ETH group (M. Dittmar et al.):(Phys. Lett. B583 (2004) 111, talk at SUSY/BSM meeting (17 Sept. 2003))

• Study focused on observables other than Mµ+µ−.• Tools: PYTHIA; no details given on how the stated mass reach was obtained.• Conclusion: “reconfirm the known Z′ boson LHC discovery potential, to reach

masses up to about 5 TeV for a luminosity of 100 fb-1”.

Previous studies of CMS discovery potential (II)


Comparison with previous studiesThis study has two main advantages:• Full simulation and reconstruction of signal and background;

therefore, takes into account:– Trigger and track-finding inefficiencies;– Charge misassignment;– Details of detector acceptance;– Momentum and mass resolution, etc.

• Appropriate statistical techniques to quantify the mass reach.

We believe it gives somewhat more justifiable estimates of CMS discovery potential in Z′ → µ+µ− channel, while still

suffering from the lack of systematic errors.


Summary• We have set up a procedure for studying and quantifying the

Z′ mass reach. Main points:– Full simulation (CMSIM) and reconstruction (ORCA6) as input;– Unbinned M.L. fits exploring signal and background shapes only;– Likelihood-ratio significance estimator, shown to perform as desired.

• We have obtained mass reach estimates in Z′ → µ+µ− channel, with systematic uncertainties yet to be accounted for:

– More than 5σ significance above 1 TeV at the earliest stages of data-taking;

– Average 5σ significance at a mass of 3.7-4.7 TeV (depending on the model) with an integrated luminosity of 100 fb-1.

• Plan to evaluate systematic uncertainties and their impact, and improve/check other items mentioned earlier.


Acknowledgements• We would like to thank all the members of CMS who

contributed to the software packages used in this study.

• We are particularly grateful to:– Norbert Neumeister, for his assistance and numerous useful

discussions on reconstruction-related issues.– Our referees (Marcos Cerrada, Marcella Diemoz, and Stefano

Lacaprara), for careful reading of the note and helpful commentsand questions.


Backup slides follow


Background-only mass fits: significance

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Overflow 584

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ScL ScL_recEntries 1000000

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Mean 0.2879

RMS 0.499

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Mean 0.2879

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Mean 0.2334

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Mean 0.3318


Overflow 0

SL

Background to 5 TeV Z′ (300 fb-1)

too many events in the tails

Observed:SL > 3: 1343 eventsSL > 4: 36 eventsSL > 5: 0 events

BS NN1,000,000 MC experiments<Nevt> above 3 TeV: 7.0<Nevt> within m0 ± 2σm: 1.4

SL

Sc12

ScL

Sc2

Expected for a Gaussian:Above 3σ: 1350 eventsAbove 4σ: 31.5 eventsAbove 5σ: 0.3 events


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Example at 3 TeV: ZSSM at 10 fb-1

”Non-fluctuating” mass spectra:(stat. much larger than expected)

generated and reconstructedZ′

DY Z′DY


SL = 5.6

σm = 5.7%

S+B fit

B-only fit

SL = 10.1


0 5 10 15 20 25 30 35 40 45 500

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Mean 27.9

RMS 8.269

Underflow 0

Overflow 0

/ ndf 2χ 9.764 / 19

Prob 0.9585

Constant 0.1423± 0.5473

Mean 1.797± 28

Sigma 1.364± 8.424

Sc1

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Entries 23

Mean 4.289

RMS 0.4763

Underflow 0

Overflow 0

/ ndf 2χ 2.157 / 1

Prob 0.142

Constant 2.346± 9.184

Mean 0.1042± 4.272

Sigma 0.07362± 0.4995

Sc2

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Entries 23

Mean 7.389

RMS 0.9771

Underflow 0

Overflow 0

/ ndf 2χ 5.545 / 5

Prob 0.353

Constant 1.179± 4.616

Mean 0.2072± 7.402

Sigma 0.1465± 0.9938

Sc12

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Entries 23

Mean 8.984

RMS 1.382

Underflow 0

Overflow 0

/ ndf 2χ 4.877 / 8

Prob 0.7707

Constant 0.8526± 3.339

Mean 0.2865± 8.989

Sigma 0.2025± 1.374

SL

ZSSM at 3 TeV, 10 fb-1: significance

• Sc1 >> SL

• Sc2 < SL

• Sc12 ~ SL

for all Z′ models, masses,

luminosities tried

b

s

NN

bs

s

NNN

+

)

(2

b

bs

N

NN

−

+×LS

Bartsch and Quast also found that Sc1 badly overestimates true S

Fix both m0 and FWHM to true values to calculate SL


Z′ at 3 TeV: SL significance

4.72.92.31.91.53.92 fb-1

OPT

9.05.74.73.53.27.710 fb-1

GMR

10.66.65.54.33.68.910 fb-1

OPT

ZALRMZLRMZχZηZψZSSM∫L·dt

• For 10 fb-1, S is more than 5 for most of the Z′ models considered;• For 2 fb-1, S is less than 5 for all models;

– SL scales nicely with • TMR reconstruction of high-pT muons helps (~ 15% gain).

intL


mu+ mu- mass3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/100

GeV

/100

fb

-1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


mu+ mu- mass3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/100

GeV

/100

fb

-1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


mu+ mu- mass3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/40

GeV

/100

fb

-1

0

0.2

0.4

0.6

0.8

1


Entries 4

Mean 3540

RMS 375


mu+ mu- mass3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/100

GeV

/100

fb

-1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

True (PYTHIA) mass

mu+ mu- mass3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/100

GeV

/100

fb

-1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

True (PYTHIA) mass

Example at 5 TeV: Zψ at 100 fb-1

”Non-fluctuating” mass spectra:(stat. much larger than expected)

generated and reconstructedZ′

DYZ′

DY


SL = 0.7

σm = 8.5%

S+B fitmu+ mu- mass

3000 3500 4000 4500 5000 5500 6000 6500 7000

Eve

nts

/40

GeV

/100

fb

-1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Entries 3

Mean 4334

RMS 733.1


SL = 2.4

B-only fit

Background flattens out with mass; how

well can it be controlled?


Z′ at 5 TeV: SL significance

6.83.93.32.82.45.2300 fb-1

OPT

3.01.71.41.21.22.3100 fb-1

GMR

3.92.21.81.61.42.9100 fb-1

OPT

ZALRMZLRMZχZηZψZSSM∫L·dt

• For 100 fb-1, S is less than 5 for all Z′ models considered;• For 300 fb-1, S is still less than 5 for most of the models;• Again, TMR reconstruction results in a higher S (by ~ 30%) .

detection of z gauge bosons in the di-muon decay...

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