David M. Webber For the MuLan Collaboration University of Wisconsin-Madison Formerly University of Illinois at Urbana-Champaign DPF Meeting, August 2011 A part-per-million measurement of the positive muon lifetime and determination of the Fermi constant 1

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 2D. 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)

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) 3D. M. Webber

MuLan collected two datasets, each containing 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, 2006Quartz Target, D. M. Webber

Leading systematic considerations: Challenging 5D. M. Webber

170 scintillator tile pairs readout using 450 MHz waveform digitizers. 2 Analog Pulses Waveform Digitizers 1/6 of system 1 clock tick = 2.2X ns 6D. M. Webber x2 ~0.1%

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 Carefully studied over the summer of Gain correction is 0.5 ppm shift with 0.25 ppm uncertainty. 7D. M. Webber

Raw waveforms are fit with templates to find pulse amplitudes and times Normal Pulse >2 x pulses in 2006 data set >65 TBytes raw data 8D. M. Webber Two pulses close together A difficult fit inner outer ADT Template

Leading order pileup to a ~5x10 -4 effect Measured  vs. Deadtime Raw Spectrum Pileup Corrected Statistically reconstruct pileup time distribution Fit corrected distribution Fill i Fill i+1  –   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 –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 10D. M. Webber

The pileup corrections were tested with Monte-Carlo. D. M. Webber11 Monte-Carlo Simulation, events agrees 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 12D. M. Webber12D. M. Webber Pileup Correction Uncertainty: 0.2 ppm

13D. M. Webber 2006: Ferromagnetic target, fit to pileup-corrected data. 22  s ppm   +  secret 2007: Quartz target data fits well as a simple sum, exploiting the symmetry of the detector. The  SR remnants vanish.

Variations in    vs. fit start time are within allowed statistical deviations D. M. Webber14

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 15D. M. Webber

Results The Result  (R06) = ± 2.5 ± 0.9 ps  (R07) = ± 3.7 ± 0.9 ps  (Combined) = ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps New G F G F (MuLan) = (7) x GeV -2 (0.6 ppm) 16D. M. Webber

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 17D. M. Webber

In hydrogen:   - )-(1/   + ) =  S  g P now in even better agreement with ChPT * * Chiral Perturbation Theory Using previous   world average 18 Shifts the MuCap result Using new MuLan   average 18D. M. Webber

MuLan Collaborators D. M. Webber 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

Summary MuLan has finished –PRL published. Phys. Rev. Lett. 106, (2011) –1.0 ppm final error achieved, as proposed –PRD in preparation Most precise lifetime –Most precise Fermi constant, 0.6 ppm Influence on muon capture –Shift moves g P to better agreement with theory –“Eliminates” the error from the positive muon lifetime, needed in future  - capture determinations (e.g. MuCap and MuSun)  (R06) = ± 2.5 ± 0.9 ps  (R07) = ± 3.7 ± 0.9 ps  (Combined) = ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps G F (MuLan) = (7) x GeV -2 (0.6 ppm) 20D. M. Webber

Backup

The predictive power of the Standard Model depends on well-measured input parameters What are the fundamental electroweak parameters (need 3)? 8.6 ppm ppm23 ppm650 ppm360 ppm  GFGF MZMZ sin 2  w MWMW Obtained from muon lifetime Other input parameters include fermion masses, and mixing matrix elements: CKM – quark mixing PMNS – neutrino mixing * circa 2000

For 1ppm, need more than 1 trillion (10 12 ) muons... πE3 Beamline, Paul Scherrer Institute, Villigen, Switzerland 23D. M. Webber

Gain is photomultiplier tube type dependent D. M. Webber24 Deviation at t=0 Artifact from start signal  s 1 ADC = V Sag in tube response

pileup Introducing higher-order pileup D. M. Webber25 hit time Artificial deadtime hit time Artificial deadtime Inner tile Outer tile Artificial deadtime triple ABCDEFG

Explanations of R vs. ADT slope Gain stability vs.  t? –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. Webber26

The push – pull of experiment and theory Muon lifetime is now the largest uncertainty on G F ; leads to 2 new experiments launched: MuLan & FAST PSI, but very different techniques –Both aim at “ppm” level G F determinations –Both published intermediate results on small data samples n Meanwhile, more theory updates !! 27D. M. Webber