David M. WebberFor the MuLan Collaboration

University of Wisconsin-MadisonFormerly University of Illinois at Urbana-Champaign

August 12, 2011

A part-per-million measurement of the positive muon lifetime and determination of the Fermi constant

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

3D. 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)

Kicker On

Fill Period

Measurement Period

The experimental concept…

time

Num

ber (

log

scal

e)

-12.5 kV

12.5 kV

Real data170 Inner/Outer

tile pairs

MHTDC(2004)

450 MHzWaveFormDigitization(2006/07)

MuLan collected two datasets, each containing 1012 muon decays

• Two (very different) data sets– Different muon stopping targets– 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

Leading systematic considerations:Cha

lleng

ing

170 scintillator tile pairs readout using 450 MHz waveform digitizers.

2 Analog PulsesWaveform Digitizers

1/6 of system

1 clock tick = 2.2 ns

7D. M. Webber

x2

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

8

4100.3N

δN

0 10 20 ms

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

Carefully studied over the summer of 2010. Gain correction is 0.5 ppm shift with 0.25 ppm uncertainty.

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

9D. M. Webber

Two pulses close together

A difficult fitinner

outer

ADTTemplate

Leading order pileup to a ~5x10-4 effect

Measured t vs. Deadtime

Raw Spectrum

Pileup Corrected

• Statistically reconstruct pileup time distribution• Fit corrected distributionFill i

Fill i+1

1/t – 2/t

2/t Pileup Time Distribution

Normal Time Distribution

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 12

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

13D. 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 14

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

22 ms

ppm tm + Dsecret

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

Variations in tm vs. fit start time are within allowed statistical deviations

D. M. Webber 16

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

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

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

Results

The Result

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

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

New GF

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

The lifetime difference between tm+ and tm in hydrogen leads to the singlet capture rate LS

log(

coun

ts)

timeμ+μ –

%16.0D + mmt

1.0 ppm MuLan ~10 ppm MuCap

m ++m np

MuCap nearly complete

gP 11 )()( ++ LLL

mmmmttS

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

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

*Chiral Perturbation Theory

Using previous tm world average

20

Shifts the MuCap result

Using new MuLan tm average

MuLan Collaborators

20072006

2004

21D. M. Webber

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

Conclusions• MuLan has finished

– PRL published. Phys. Rev. Lett. 106, 041803 (2011)– 1.0 ppm final error achieved, as proposed– PRD in preparation

• Most precise lifetime– Most precise Fermi constant

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

future m- capture determinations (e.g. MuCap and MuSun) t(R06) = 2 196 979.9 ± 2.5 ± 0.9 ps t(R07) = 2 196 981.2 ± 3.7 ± 0.9 ps

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

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

Backup

D. M. Webber 23

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

πE3 Beamline, Paul Scherrer Institute, Villigen, Switzerland

Gain is photomultiplier tube type dependent

D. M. Webber 25

Deviation at t=0

Artifact from start signal

0 10 20 ms

1 ADC = 0.004 V

Sag in tube response

pileup

Introducing higher-order pileup

D. M. Webber 26

hit

time

Artificial deadtime

hit

time

Artificial deadtimeInner tile

Outer tile

Artificial deadtime

Artificial deadtime

tripleA B C D E F G

The push – pull of experiment and theory• Muon lifetime is now the largest uncertainty on GF ;

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 !!