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A part-per-million measurement of the positive muon lifetime and determination of the Fermi constant. David M. Webber For the MuLan Collaboration University of Wisconsin-Madison Formerly University of Illinois at Urbana-Champaign August 12, 2011. - PowerPoint PPT Presentation
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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 !!