David M. Webber University of Illinois at Urbana-Champaign For the MuLan Collaboration A new determination of the positive muon lifetime to part per million precision

Motivation gives the Fermi Constant to very high precision (actually G  ) needed for “reference” lifetime for precision muon capture experiments –MuCap:  - + p –MuSun:  - + d Capture rate from lifetime difference    and   2D. M. Webber

qq In the Fermi theory, muon decay is a contact interaction where  q 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 G F from theory to < 0.3 ppm (it was the dominant error before)

Fast-switching electric kicker on Fill Period Measurement Period time Number (log scale) kV 12.5 kV Real data B 100% polarized muons at ~4 MeV Rapidly precess The experimental concept in one animation … 4D. M. Webber Kicker Systematic Uncertainty < 0.2 ppm

170 scintillator tile pairs readout using 450 MHz waveform digitizers. 2 Analog Pulses Waveform Digitizers 1/6 of system 1 clock tick = 2.2 ns 5D. M. Webber Uncertainty from electronics stability: 0.26 ppm x2

MuLan collected two datasets, each containing muon decays. Two (very different) data sets –2006: Ferromagnetic target dephases muon ensemble 1.16 ppm statistical uncertainty –2007: Quartz target forms 90% muonium, 10% free (precessing) muons 1.7 ppm statistical uncertainty 6D. M. Webber Ferromagnetic Target, 2006Quartz Target, 2007

Fits of raw waveforms using Templates A difficult fit Normal Pulse Two pulses close together >2 x / data set >135 TBytes raw data 7D. M. Webber

MPV And, in coincidence Time and Energy derived from fits of the raw waveforms Ratio cut vs MPV by run # Cut  N = 570 ppm / ADC  s /   Known electronics artifact MPV Electronics stability  0.26 ppm 8D. M. Webber (work in progress) Gain stability  ppm shift in lifetime, probably the smaller

Leading order pileup Measured  vs. Deadtime Raw Spectrum Pileup Corrected Same probability Statistically reconstruct pileup time distribution Fit corrected distribution Pileup Time Distribution Normal Time Distribution 9D. M. Webber

Pileup to sub-ppm requires higher-order terms 12 ns deadtime, pileup has a 5 x probability at our rates Proof of procedure validated with detailed Monte Carlo simulation –Over MC events generated 1 ppm 150 ns deadtime range Artificial Deadtime (ct) R (ppm) Pileup terms at different orders … uncorrected 10D. M. Webber

Lifetime vs artificially imposed deadtime window is an important diagnostic 1 ppm 150 ns deadtime range Artificial Deadtime (ct) R (ppm) A slight slope exists, which we continue to investigate Extrapolation to 0 deadtime should be correct answer and our indications are that this extrapolation is right 11D. M. Webber (Work in progress) Pileup Correction Uncertainty: 0.15—0.3 ppm

D. M. Webber R vs fit start time Red band is the set-subset allowed variance 2006: Fit of 30,000 AK-3 pileup-corrected runs 22  s ppm   +  secret Clock Ticks (1 clock tick ~ 2.2 ns) 12

2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The  SR remnants vanish. 13D. M. Webber

2007: Consistency against MANY special runs, where we varied target, magnet, ball position, etc. Start-time scan 14D. M. Webber

MuLan Systematic Uncertainties (preliminary) Source2006 (ppm)2007 (ppm) Kicker stability Errant muon stops0.1 (same as 2006) Gain stability vs time0.04 – 0.7 (same as 2006) Gain stability vs dt0.3 (same as 2006) Timing stability vs time0.014 (same as 2006) Timing stability vs dt0.02 (same as 2006) Electronic readout stability0.26 (same as 2006) Pileup correction0.15 – 0.3 (same as 2006) Residual polarizationn/a0.2 Total Systematic (0.51 common) Statistical Uncertainty   in common blinded space (compared Feb 8, 2010) Total Uncertainty: 1.1 – 1.3 ppm 15D. M. Webber For the rest of the talk I will use 1.3 ppm, but it should decrease as studies finalize.  =0.3 ppm!

New MuLan Result Lifetime value final, preliminary error will decrease MuLan 2007:   = ± 3.7(stat) ± 1.2(sys) ps G F = (7) x GeV -2 (0.6 ppm)* New world avg:   = ± 2.4 ps (1.09 ppm) 16D. M. Webber *includes 0.43 ppm shift on Δq from linear m e term (Pak & Czarnecki, 2008) MuLan 2006:   = ± 2.5(stat) ± 1.2(sys) ps

D. M. Webber17 MuLan 2004 FAST

  + )-(   - )  g P now in better agreement with ChPT * * Chiral Perturbation Theory Using previous   world averageUsing new   world average What is g P ? 18D. M. Webber

MuLan Collaborators Institutions: University of Illinois at Urbana-Champaign University of California, Berkeley TRIUMF University of Kentucky Boston University James Madison University Groningen University Kentucky Wesleyan College 19D. M. Webber

MuLan measured the muon lifetime to ppm-level precision. MuLan measurement is most precise (and accurate) W.A.   = ± 2.4 ps Lifetime value final, preliminary error will decrease –Combined uncertainty 1.1—1.3 ppm G F = (7) x GeV -2 g P better agrees with ChPT 20D. M. Webber

21D. M. Webber

Backup Slides

Effect of  on G F In the Standard Model,  =0, General form of  Drop second-order nonstandard couplings Effect on G F return 23D. M. Webber

The MuLan Collaboration A subset of the collaboration (taken at PSI in 2007) The “Precision Muon Group” at UIUC (taken in 2007) 24D. M. Webber

What is g P ? g P is the pseudoscalar form factor of the proton 25D. M. Webber

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 26D. M. Webber

νn pμ 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 27D. M. Webber

New MuLan Result Lifetime value final, preliminary error will decrease MuLan result:   = ± 2.9 ps (1.3 ppm) 2008: G F = (5) x GeV -2 (4.1 ppm)* (from world avg) 2010: G F = (7) x GeV -2 (0.6 ppm)** New world avg:   = ± 2.8 ps (1.3 ppm) 28D. M. Webber *derived solely from MuLan 2010 *includes 0.43 ppm shift on Δq from linear m e term (Pak & Czarnecki, 2008)

Correcting vs. fitting for pileup Fitting for pileup shortens the lifetime by 3 ppm. Fitting for pileup is less robust than correcting for pileup. Pileup corrected before fitPileup included in fit 29D. M. Webber

Analysis code cross-checks Monte-Carlo Simulation events Histogramming code: Monte-Carlo Pileup Correction agrees with truth Pulse Fitting Code: Two independent fitters agree Using 1% subset of data 1% acceptance difference Production Fitter Independent code check 30D. M. Webber

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 31D. M. Webber

Depolarizing the Muons 2006 AK3 target ferromagnetic high internal magnetic field 2007 Quartz Target polarization preserving applied external field 32D. M. Webber

Lifetime stable even though we rolled the ball away from the target – shows dephasing works Inside radius of Ball 33D. M. Webber

“Precision” History of G F (contributions from theory and muon lifetime) MuLan Goal MuLan 2007 FAST D. M. Webber

e+e+  Positron energy distribution E e = 26.4 MeV E e = 13.2 MeV Detection threshold E e = E max = MeV Polarization Issues Detector constructed such that opposite pair summation cancels polarization asymmetries up to acceptance differences 35D. M. Webber

Hardware and systematic analysis led by Peter Winter (an Illinois postdoc currently at PSI) Extinction ~ 1000 Trigger Suppression Accumulation Period Measuring Period counts arb. A better beam tune and more detailed kicker measurements give a 0.2 ppm (0.1 ppm in 2007) uncertainty on kicker stability. 36D. M. Webber

Gain and time stability checked in-situ with laser pulses. Laser time – Detector time Time in fill (ct) Detector Height / Laser Height 0.04 ppm 0.02 ppm Analysis by Brett Wolfe (former undergraduate) 37D. M. Webber

Precision Clock System The clock is tunable, but the analyzers only know the 4 most significant digits (500 ppm) Checked weekly for consistency throughout the run. Rubidium Atomic Clock MuLan Agilent Clock Error 60 MHz MHz20 ppb 30 MHz MHz20 ppb Agilent E4400 Function Generator 38D. M. Webber

18 ppm0.09 ppm30 ppmMid 90s:17 ppm8.1 ppm< 0.3 ppm2008:4.1 ppm What are the uncertainties? ~1 ppm< 0.3 ppmGoal:~0.5 ppm Aside:  39D. M. Webber

A. Pak and A. Czarnecki: Linear m e term gives ppm shift on Δq (June 2008) 18 ppm0.09 ppm< 0.3 ppm1999:9 ppm The Standard Model Fermi extraction is no longer theory limited. MuLan R04 MuLan Goal MuLan R04 Theoretical uncertainty 18 ppm0.09 ppm30 ppmMid 90s:17 ppm 0.09 ppm8.1 ppm< 0.3 ppmNow:4.1 ppm Uncertainty on the muon lifetime error now limits the uncertainty on G F. G F uncertainty 2 exp. efforts: MuLan & FAST 40D. M. Webber

Method accounting for  SR is preferred. Precession characteristics in each detector are observed and included in the fit function: Difference between Top of Ball and Bottom of Ball to Sum, vs time-in-fill 41D. M. Webber

Because of any small residual longitudinal polarization, each fit gives an “effective” lifetime based on the position with respect to the external field. The ensemble is then fit to obtain the actual lifetime. (Method robust in MC studies) Magnet-right data 42D. M. Webber

ARNOKROME™ III (AK-3) high-field ferromagnetic target used in Rapid precession of muon spin -  SR studies show fast damping Target rotates out of beam 43

In 2007 we used a crystal quartz target and an external ~ 135 G magnetic field 90% muonium formation –“test” of lifetime in muonium vs. free –Rapid spin precession 10% “free” muons –These precess in a noticeable manner and create an analysis challenge Magnet ring “shadows” part of detector Installed Halbach Array Quartz 44D. M. Webber

New MuLan Result Lifetime value final, preliminary error will decrease MuLan result:   = ± 2.9 ps (1.3 ppm) 2008: G F = (5) x GeV -2 (4.1 ppm)* (from world avg) 2010: G F = (7) x GeV -2 (0.6 ppm)** New world avg:   = ± 2.8 ps (1.3 ppm) 45D. M. Webber *derived solely from MuLan 2010 *includes 0.43 ppm shift on Δq from linear m e term (Pak & Czarnecki, 2008)