Measurement of the Positive Muon Lifetime and Determination of the Fermi Constant to Part-per-Million Precision David Hertzog University of Washington* for the MuLan Collaboration *Our Illinois group just moved to the University of Washington – the CENPA Laboratory I am stepping in for Volodya Tishchenko who was delayed by passport processing issues. He’ll be here soon for our MuSun run The Result

determined Fermi Constant to unprecedented precision (actually G  ) needed for “reference” lifetime for precision muon capture experiments –MuCap  g P –MuSun  L 1A Is lifetime in bound muonium the same as the free lifetime? MuLan Motivation Capture rate from lifetime difference    and   Talk: P Winter G F  M Z 9 ppm 0.37 ppb 23 ppm 0.6 ppm

The Fermi constant is related to the electroweak gauge coupling g by In the Fermi theory, muon decay is a contact interaction where  q is phase space and both QED and hadronic and radiative corrections q Contains all weak interaction loop corrections In 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in G F from theory to < 0.3 ppm (it was the dominant error before)

The push – pull of experiment and theory n Lifetime now largest uncertainty leads to 2 new experiments launched: MuLan & FAST u PSI, but very different techniques u Both aim at “ppm” level G F determinations u Both published intermediate results on small data samples n n Meanwhile, more theory updates !!

G F &   precision has improved by ~4 orders of magnitude over 60 years. Achieved!

The lifetime difference between    and    in hydrogen leads to the singlet capture rate  S log(counts) time μ+μ+ μ – 1.0 ppm MuLan ~10 ppm MuCap MuCap nearly complete  gP gP The singlet capture rate is used to determine g P and compare with theory

Kicker On Fill Period Measurement Period The experimental concept… time Number (log scale) kV 12.5 kV Real data 170 Inner/Outer tile pairs MHTDC (2004) 450 MHz WaveForm Digitization (2006/07)

MuLan collected two datasets, each containing 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 Ferromagnetic Target, 2006Quartz Target, 2007

A difficult fit Normal Pulse Two pulses close together >2 x decays 130 TB data at NCSA “artificial” deadtimes Raw waveforms for 170 inner and outer scintillators are fit using calibrated pulse templates

Leading systematic considerations: Challenging

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  s accumulation period Muons precess by 0 to 350 revolutions  DEPHASED  small ensemble avg. polarization Ensemble Averge Polarization

Fit of 30,000 AK-3 pileup-corrected runs 22  s ppm   +  secret tau vs fit start time Red band is the set-subset allowed variance Relative  (ppm) 0 9  s

A small asymmetry exists front / back owing to residual longitudinal polarization Lifetime FrontBack Opposite pairs summed “front-back folded” When front / back opposite tile pairs are added first, there is no distortion  85 Opposite Pairs All 170 Detectors

2007 target: crystal quartz, surrounded by an external ~ 135 G magnetic field n 90% muonium formation u “Test” of lifetime in muonium vs. free u Rapid spin precession not observable by us n 10% “free” muons u Precession noticeable and small longitudinal polarization exists  Creates analysis challenges ! n 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  SR. 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 data Relative effective lifetime (ppm) (+ blind offset)

Sanity check: Same result by simple summing detectors and doing 1 fit The  SR remnants just vanish … as one would predict 17 Projection of residuals Start-time scan Relative effective lifetime (ppm) (+ blind offset)

Leading order pileup to a ~5x10 -4 effect Measured  vs. Deadtime Raw Spectrum Pileup Corrected Statistically reconstruct pileup time distribution Fit corrected distribution Pileup Time Distribution Normal Time Distribution Fill i Fill i+1  –  

Pileup to sub-ppm requires higher-order terms n 12 ns deadtime, pileup has a 5 x probability at our rates u Left uncorrected, lifetime wrong by 100’s of ppm n 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

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 20D. M. Webber Pileup Correction Uncertainty: 0.2 ppm

Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution  s If MPV moves, implies greater or fewer hits will be over threshold Gain(t) is PMT type dependent. Carefully studied over the summer and reduced to 0.25 ppm uncertainty. Gain correction gives a 0.5 ppm shift in result vs uncorrected

Final Errors and Numbers ppm units  (R06) = ± 2.5 ± 0.9 ps  (R07) = ± 3.7 ± 0.9 ps  (Combined) = ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps

Lifetime “history” New G F G F (MuLan) = (7) x GeV -2 (0.6 ppm) The most precise particle or nuclear or (we believe) atomic lifetime ever measured FAST

In hydrogen:   - )-(1/   + ) =  S  g P now in even better agreement with ChPT * * Chiral Perturbation Theory Using previous   world average 24 Shifts the MuCap result Using new MuLan   average

MuLan at PSI

Conclusions n MuLan has finished u PRL submitted u 1.0 ppm final error achieved, as proposed n Most precise lifetime u Most precise Fermi constant u “Modest” check of muonium versus free muon n Influence on muon capture u Shift moves g P to better agreement with theory u “Eliminates” the error from the positive muon lifetime, needed in future MuCap and MuSun capture determinations  (R06) = ± 2.5 ± 0.9 ps  (R07) = ± 3.7 ± 0.9 ps  (Combined) = ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps