David M WebberUniversity of Illinois at Urbana-Champaign

(Now University of Wisconsin-Madison)December 9, 2010

A PART-PER-MILLION MEASUREMENT OF THE POSITIVE MUON LIFETIME AND DETERMINATION OF

THE FERMI CONSTANT

Outline• Motivation• Experiment Hardware• Analysis

– Pulse Fitting– Fit Results

• Systematic Uncertainties– Gain Stability– Pileup– Spin Rotation

• Final Results

D. M. Webber 2

Motivation

• gives the Fermi Constant to unprecedented precision (actually Gm)

• needed for “reference” lifetime for precision muon capture experiments– MuCap– MuSun

m

m

Capture rate from lifetime difference m- and m

The predictive power of the Standard Model depends on well-measured input parameters

What are the fundamental electroweak parameters (need 3)?

8.6 ppm0.00068 ppm 23 ppm 650 ppm 360 ppma GF MZ sin2qw MW

Obtained from muon lifetime

Other input parameters include fermion masses, and mixing matrix elements:CKM – quark mixing

PMNS – neutrino mixing

* circa 2000

Dq

In the Fermi theory, muon decay is a contact interaction where Dq includes phase space, QED, hadronic and radiative corrections

The Fermi constant is related to the electroweak gauge coupling g by

Contains all weak interaction loop corrections

5D. M. Webber

In 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in GF from theory to < 0.3 ppm (it was the dominant error before)

The push – pull of experiment and theory• Lifetime now largest uncertainty leads to 2 new

experiments launched: MuLan & FAST– Both @ PSI, but very different techniques– Both aim at “ppm” level GF determinations– Both published intermediate results on small data samples

Meanwhile, more theory updates !!

The lifetime difference between m and m- in hydrogen leads to the singlet capture rate LS

log(

coun

ts)

timeμ+μ –

%16.0D - - mm

1.0 ppm MuLan ~10 ppm MuCap

m- m np

MuCap nearly complete

gP 11 )()( ---- -L-LL

mmmmS

The singlet capture rate is used to determine gP and compare with theory

Experiment

D. M. Webber 10

For 1ppm, need more than 1 trillion (1012) muons ...

πE3 Beamline, Paul Scherrer Institut, Villigen, Switzerland

The beamline transports ~107 “surface” muons per second to the experimental area.

MomentumSelection

%2Dpp

Parallel beam

Velocity separator removes beam positrons

Spatial focus

A kicker is used to create the time structure.

22 ms 5 ms

Extinction ~ 1000Trigger Suppression

AccumulationPeriod

Measuring Period kicker

coun

ts a

rb.

ARNOKROME™ III (AK-3) high-field target used in 2006 - Rapid precession of muon spin - mSR studies show fast damping

The target was opened once per day to view the beam profile.

D. M. Webber 15

Target rotates out of beam

In 2006, The ferromagnetic target dephases the muons during accumulation.

• Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron)• 0.5 T internal magnetic field• Muons arrive randomly during 5 ms accumulation period• Muons precess by 0 to 350 revolutions

16D. M. Webber

2007 target: crystal quartz, surrounded by an external ~ 135 G magnetic field

• 90% muonium formation – “Test” of lifetime in muonium vs. free– Rapid spin precession not observable by us

• 10% “free” muons– Precession noticeable and small longitudinal polarization exists

• Creates analysis challenges !• Magnet ring “shadows” part of detector

Installed

Halbach Array

Quartz

Kicker On

Fill Period

Measurement Period

The experimental concept…

time

Num

ber (

log

scal

e)

-12.5 kV

12.5 kV

Real data

170 Inner/Outertile pairs

MHTDC(2004)

450 MHzWaveFormDigitization(2006/07)

Each section contains either 6 or 5tile elements

a

Each element is made from two independentscintillator tiles with light guides and photomultiplier tubes.

The detector is composed of 20 hexagonand 10 pentagon sections, forming a truncated icosahedron.

170 scintillator tile pairs readout using 450 MHz waveform digitizers.

2 Analog PulsesWaveform Digitizers

1/6 of system

1 clock tick = 2.2 ns

20D. M. WebberUncertainty on lifetime from gain stability: 0.25 ppm

x2

• Checked for consistency throughout the run.

• Compared to Quartzlock A10-R rubidium frequency standard.

• Compared to calibrated frequency counter

• Different blinded frequencies in 2006 and 2007

Agilent E4400 Function Generator

f = 450.87649126 MHz

The clock was provided by an Agilent E4400B Signal Generator, which was stable during the run and found to be accurate to 0.025 ppm.

Average difference = 0.025 ppm

f = 451.0 +/- 0.2

MuLan collected two datasets, each containing 1012 muon decays

• Two (very different) data sets– Different blinded clock frequencies used– Revealed only after all analyses of both data sets completed– Most systematic errors are common– Datasets agree to sub-ppm

Ferromagnetic Target, 2006 Quartz Target, 2007

Analysis

D. M. Webber 23

Raw waveforms are fit with templates to find pulse amplitudes and times

Normal Pulse

>2 x 1012 pulses in 2006 data set >65 TBytes raw data

25D. M. Webber

Two pulses close together

A difficult fitinner

outer

ADTTemplate

Nearby pulses perturb the time of main pulses.Studied with simulations

D. M. Webber 26

Fixed reference

perturbation Dtavg

Dtavg Estimated pull:

ppm075.0)/ct1000(

)pileup%25.0()ct03.0(

m

2006: Fit of 30,000 AK-3 pileup-corrected runs.

22 ms

ppm m + Dsecret

R vs fit start timeRed band is the set-subset allowed variance

Relative (ppm)

0 9 ms

2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish.

Systematics

Introduction

D. M. Webber 29

Leading systematic considerations:Cha

lleng

ing

Systematics:Gain Stability

D. M. Webber 31

Gain is photomultiplier tube type dependent

D. M. Webber 32

Deviation at t=0

Artifact from start signal

0 10 20 ms

1 ADC = 0.004 V

Sag in tube response

Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution

33

4100.3N

δN -

0 10 20 ms

If MPV moves, implies greater or fewer hits will be over threshold

Carefully studied over the summer. Gain correction is 0.5 ppm shift with 0.25 ppm uncertainty.

Systematics:Pileup

D. M. Webber 34

Leading order pileup to a ~5x10-4 effect

Measured vs. Deadtime

Raw Spectrum

Pileup Corrected

• Statistically reconstruct pileup time distribution• Fit corrected distributionFill i

Fill i+1

1/ – 2/

2/ Pileup Time Distribution

Normal Time Distribution

pileup

Introducing higher-order pileup

D. M. Webber 36

hit

time

Artificial deadtime

hit

time

Artificial deadtimeInner tile

Outer tile

Artificial deadtime

Artificial deadtime

tripleA B C D E F G

Pileup to sub-ppm requires higher-order terms• 12 ns deadtime, pileup has a 5 x 10-4 probability at our rates

– Left uncorrected, lifetime wrong by 100’s of ppm• Proof of procedure validated with detailed Monte Carlo simulation

1 ppm

150 ns deadtime range

Artificial Deadtime (ct)

R (ppm)

Pileup terms at different orders …

uncorrected

The pileup corrections were tested with Monte-Carlo.

D. M. Webber 38

Monte-Carlo Simulation, 1012 eventsagrees with truth to < 0.2 ppm

1.19 ppm statistical uncertainty

Lifetime vs. artificially imposed deadtime window is an important diagnostic

1 ppm

150 ns deadtime range

• A slope exists due to a pileup undercorrection

Extrapolation to 0 deadtime is correct answer

39D. M. WebberPileup Correction Uncertainty: 0.2 ppm

Explanations of R vs. ADT slope

• Gain stability vs. Dt? – No. Included in gain stability systematic uncertainty.

• Missed correction?– Possibly– Extrapolation to ADT=0 valid

• Beam fluctuations?– Likely– Fluctuations at 4% level in ion source exist– Extrapolation to ADT=0 valid

D. M. Webber 40

Systematics

Spin Precession

D. M. Webber 41

• Highest energy positron when neutrinos are parallel.

• Neutrino helicities cancel angular momentum.

• Positron spin must be in the same direction as muon spin.

• Chiral limit dictates right handed positrons.

• Most probable positron direction is same as muon spin

• Lowest energy positron when neutrinos are anti-parallel.

• Neutrino helicities add so that they have angular momentum of 2.

• Positron spin must compensate to bring total to 1.

• Chiral suppression (not well justified at this energy) makes positron most likely right handed.

• Most probable positron direction is opposite muon spin

e+

q

The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates.

maxEEx e

Ee = Emax = 52.83 MeV

Positron energy distribution

Ee = 26.4 MeVEe = 13.2 MeV

Detectionthreshold

Highest Energy PositronsLowest Energy Positrons

mSR rotation results in an oscillation of the measurement probability for a given detector.

B = 34 G B = 1 G

cmeBg

mm

2

This oscillation is easily detected This oscillation is not easily detectedand systematic errors may arise

2mg

- tcos1/exp)( 0 PatNtN

Bm

coun

ts a

rb.

coun

ts a

rb.

The sum cancels muSR effects; the difference accentuates the effect.

Sum Difference/Sum

Bm

coun

ts a

rb.

coun

ts a

rb.

coun

ts a

rb.

2006 target: AK3 ferromagnetic alloy with high internal magnetic field

• Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron)

• 0.4 T transverse field rotates muons with 18 ns period

• Muons arrive randomly during 5 ms accumulation period

• Muons precess by 0 to 350 revolutions DEPHASED small ensemble avg. polarization

Ense

mbl

e Av

erge

Pol

ariz

atio

n

A small asymmetry exists front / back owing to residual longitudinal polarization

Life

time

Front Back

Opp

osite

pai

rs s

umm

ed

“front-back folded”

When front / back opposite tile pairs are added first, there is no distortion

m

85 Opposite PairsAll 170 Detectors

2007 target: crystal quartz, surrounded by an external ~ 135 G magnetic field

• 90% muonium formation – “Test” of lifetime in muonium vs. free– Rapid spin precession not observable by us

• 10% “free” muons– Precession noticeable and small longitudinal polarization exists

• Creates analysis challenges !• Magnet ring “shadows” part of detector

Installed

Halbach Array

Quartz

Difference between Top of Ball and Bottom of Ball to Sum, vs time-in-fill

We directly confront the mSR. Fit each detector for an “effective lifetime.” Would be correct, except for remnant longitudinal polarization relaxation.

Illustration of free muon precession in top/bottom detector differences

Longitudinal polarization distorts result in predictable manner depending on location. The ensemble of lifetimes is fit to obtain the actual lifetime. (Method robust in MC studies)

Magnet-right dataRelative effective lifetime (ppm) (+ blind offset)

2007: Consistency against MANY special runs, where we varied target, magnet, ball position, etc.

Start-time scan

Consistency Checks

D. M. Webber 53

2006: Fit of 30,000 AK-3 pileup-corrected runs

22 ms

ppm m + Dsecret

R vs fit start timeRed band is the set-subset allowed variance

Relative (ppm)

0 9 ms

2006: AK-3 target consistent fits of individual detectors, but opposite pairs – summed – is better

Difference of Individual lifetimes to average

85 Opposite PairsAll 170 Detectors

2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish

Variations in m vs. fit start time are within allowed statisical deviations

D. M. Webber 57

Conclusions

D. M. Webber 58

Final Errors and Numbers

Effect 2006 2007 Comment Kicker extinction stability 0.20 0.07 Voltage measurements of plates Residual polarization 0.10 0.20 Long relax; quartz spin cancelation Upstream muon stops 0.10 Upper limit from measurements Overall gain stability: 0.25 MPV vs time in fill; includes: Short time; after a pulse MPVs in next fill & laser studies Long time; during full fill Different by PMT type Electronic ped fluctuation Bench-test supported Unseen small pulses Uncorrected pileup effect gain Timing stability 0.12 Laser with external reference ctr. Pileup correction 0.20 Extrapolation to zero ADT Clock stability 0.03 Calibration and measurement Total Systematic 0.42 0.42 Highly correlated for 2006/2007 Total Statistical 1.14 1.68

ppm units

(R06) = 2 196 979.9 ± 2.5 ± 0.9 ps(R07) = 2 196 981.2 ± 3.7 ± 0.9 ps

(Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)D(R07 – R06) = 1.3 ps

GF & m precision has improved by ~4 orders of magnitude over 60 years.

Achieved!

Lifetime “history”

New GF

GF(MuLan) = 1.166 378 8(7) x 10-5 GeV-2 (0.6 ppm)

The most precise particle or nuclear or (we believe) atomic lifetime ever measured

FAST

The lifetime difference between m and m- in hydrogen leads to the singlet capture rate LS

log(

coun

ts)

timeμ+μ –

%16.0D - - mm

1.0 ppm MuLan ~10 ppm MuCap

m- m np

MuCap nearly complete

gP 11 )()( ---- -L-LL

mmmmS

The singlet capture rate is used to determine gP and compare with theory

In hydrogen: 1/m-)-(1/m+) = LS gP now in even better agreement with ChPT*

*Chiral Perturbation Theory

Using previous m world average

64

Shifts the MuCap result

Using new MuLan m average

Conclusions• MuLan has finished

– PRL accepted and in press. (see also arxiv:1010.0991)– 1.0 ppm final error achieved, as proposed

• Most precise lifetime– Most precise Fermi constant– “Modest” check of muonium versus free muon

• Influence on muon capture– Shift moves gP to better agreement with theory– “Eliminates” the error from the positive muon lifetime, needed in

future MuCap and MuSun capture determinations

(R06) = 2 196 979.9 ± 2.5 ± 0.9 ps (R07) = 2 196 981.2 ± 3.7 ± 0.9 ps

(Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm) D(R07 – R06) = 1.3 ps

MuLan Collaborators

20072006

2004

66D. M. Webber

Institutions:University of Illinois at Urbana-ChampaignUniversity of California, BerkeleyTRIUMFUniversity of KentuckyBoston UniversityJames Madison UniversityGroningen UniversityKentucky Wesleyan College

D. M. Webber 67

Backup Slides

What is gP?gP is the pseudoscalar form factor

of the proton

69D. M. Webber

LGFVud2

a (1- 5)m da (1- 5)u

d

uμ

At a fundamental level, the leptonic and quark currents possess the simple V−A structure characteristic of the weak interaction.

ν

Muon capture

70D. M. Webber

ν n

pμ

pgqggqign PAMV )()()()( 55 aa

aa

In reality, the QCD substructure of the nucleon complicates the weak interaction physics. These effects are encapsulated in the nucleonic charged current’s four “induced form factors”:

Muon capture

Return 71D. M. Webber

Miscellaneous

D. M. Webber 72

• Highest energy positron when neutrinos are parallel.

• Neutrino helicities cancel angular momentum.

• Positron spin must be in the same direction as muon spin.

• Chiral limit dictates right handed positrons.

• Most probable positron direction is same as muon spin

• Lowest energy positron when neutrinos are anti-parallel.

• Neutrino helicities add so that they have angular momentum of 2.

• Positron spin must compensate to bring total to 1.

• Chiral suppression (not well justified at this energy) makes positron most likely right handed.

• Most probable positron direction is opposite muon spin

e+

q

The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates.

maxEEx e

Ee = Emax = 52.83 MeV

Positron energy distribution

Ee = 26.4 MeVEe = 13.2 MeV

Detectionthreshold

Highest Energy PositronsLowest Energy Positrons

Effect of h on GF

• In the Standard Model, h=0, • General form of h • Drop second-order nonstandard couplings

• Effect on GF

return 74D. M. Webber