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![Page 1: David M Webber University of Illinois at Urbana-Champaign (Now University of Wisconsin-Madison) December 9, 2010 A PART-PER-MILLION MEASUREMENT OF THE.](https://reader036.fdocuments.in/reader036/viewer/2022070415/56649ee85503460f94bf9aaf/html5/thumbnails/1.jpg)
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
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Outline• Motivation• Experiment Hardware• Analysis
– Pulse Fitting– Fit Results
• Systematic Uncertainties– Gain Stability– Pileup– Spin Rotation
• Final Results
D. M. Webber 2
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Motivation
• gives the Fermi Constant to unprecedented precision (actually Gm)
• needed for “reference” lifetime for precision muon capture experiments– MuCap– MuSun
Capture rate from lifetime difference m- and m+
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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 ppm
a 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
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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)
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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 !!
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The lifetime difference between tm+ and tm- in hydrogen leads to the singlet capture rate LS
log
(co
un
ts)
timeμ+
μ –
%16.0
1.0 ppm MuLan
~10 ppm MuCap
np
MuCap nearly complete
gP 11 )()(
S
The singlet capture rate is used to determine gP and compare with theory
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Experiment
D. M. Webber 10
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For 1ppm, need more than 1 trillion (1012) muons ...
πE3 Beamline, Paul Scherrer Institut, Villigen, Switzerland
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The beamline transports ~107 “surface” muons per second to the experimental area.
MomentumSelection
%2pp
Parallel beam
Velocity separator removes beam positrons
Spatial focus
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A kicker is used to create the time structure.
22 ms 5
ms
Extinction ~ 1000Trigger Suppression
Accumulation
PeriodMeasuring Period kicker
coun
ts a
rb.
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ARNOKROME™ III (AK-3) high-field target used in 2006 - Rapid precession of muon spin - mSR studies show fast damping
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The target was opened once per day to view the beam profile.
D. M. Webber 15
Target rotates out of beam
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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
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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
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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)
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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.
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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
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• 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
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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
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Analysis
D. M. Webber 23
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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
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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(
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2006: Fit of 30,000 AK-3 pileup-corrected runs.
22 ms
ppm tm + Dsecret
R vs fit start timeRed band is the set-subset allowed variance
Relative t (ppm)
0 9 ms
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2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish.
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Systematics
Introduction
D. M. Webber 29
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Leading systematic considerations:C
halle
ngin
g
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Systematics:Gain Stability
D. M. Webber 31
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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
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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.
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Systematics:Pileup
D. M. Webber 34
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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
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pileup
Introducing higher-order pileup
D. M. Webber 36
hit
time
Artificial deadtime
hit
time
Artificial deadtimeInner tile
Outer tile
Artificial deadtime
Artificial deadtime
triple
A B C D E F G
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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
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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
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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
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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
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Systematics
Spin Precession
D. M. Webber 41
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• 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
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mSR rotation results in an oscillation of the measurement probability for a given detector.
B = 34 G B = 1 G
cm
eBg
2
This oscillation is easily detected This oscillation is not easily detectedand systematic errors may arise
2g
tcos1/exp)( 0 PatNtN
B
coun
ts a
rb.
coun
ts a
rb.
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The sum cancels muSR effects; the difference accentuates the effect.
Sum Difference/Sum
B
coun
ts a
rb.
coun
ts a
rb.
coun
ts a
rb.
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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
En
sem
ble
Ave
rge
Po
lari
zati
on
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A small asymmetry exists front / back owing to residual longitudinal polarization
Lif
etim
e
Front Back
Op
po
site
pai
rs s
um
med
“front-back folded”
When front / back opposite tile pairs are added first, there is no distortion
85 Opposite PairsAll 170 Detectors
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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
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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
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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)
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2007: Consistency against MANY special runs, where we varied target, magnet, ball position, etc.
Start-time scan
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Consistency Checks
D. M. Webber 53
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2006: Fit of 30,000 AK-3 pileup-corrected runs
22 ms
ppm tm + Dsecret
R vs fit start timeRed band is the set-subset allowed variance
Relative t (ppm)
0 9 ms
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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
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2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The mSR remnants vanish
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Variations in tm vs. fit start time are within allowed statisical deviations
D. M. Webber 57
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Conclusions
D. M. Webber 58
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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
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GF & tm precision has improved by ~4 orders of magnitude over 60 years.
Achieved!
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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
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The lifetime difference between tm+ and tm- in hydrogen leads to the singlet capture rate LS
log
(co
un
ts)
timeμ+
μ –
%16.0
1.0 ppm MuLan
~10 ppm MuCap
np
MuCap nearly complete
gP 11 )()(
S
The singlet capture rate is used to determine gP and compare with theory
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In hydrogen: (1/tm-)-(1/tm+) = LS gP now in even better agreement with ChPT*
*Chiral Perturbation Theory
Using previous t m world average
64
Shifts the MuCap result
Using new MuLan tm average
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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
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
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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
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D. M. Webber 67
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Backup Slides
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What is gP?gP is the pseudoscalar form factor
of the proton
69D. M. Webber
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LGFVud
2 (1 5) d (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
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ν n
pμ
pgqggqign PAMV )()()()( 55
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
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Miscellaneous
D. M. Webber 72
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• 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
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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