1. David M. Webber For the MuLan Collaboration University of Wisconsin-Madison Formerly 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

2. 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 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

3. 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)

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

5. MuLan collected two datasets, each containing 10 12 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, 2007

6. Leading systematic considerations: Challenging

7. 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 7D. M. Webber x2

8. Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution 8 0 10 20  s 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.

9. Raw waveforms are fit with templates to find pulse amplitudes and times Normal Pulse >2 x 10 12 pulses in 2006 data set >65 TBytes raw data 9D. M. Webber Two pulses close together A difficult fit inner outer ADT Template

10. 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

11. 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

12. The pileup corrections were tested with Monte-Carlo. D. M. Webber12 Monte-Carlo Simulation, 10 12 events agrees with truth to < 0.2 ppm 1.19 ppm statistical uncertainty

13. 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. Webber Pileup Correction Uncertainty: 0.2 ppm

14. 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. Webber14

15. 2006: Fit of 30,000 AK-3 pileup-corrected runs. 22  s ppm   +  secret 2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The  SR remnants vanish.

16. Variations in    vs. fit start time are within allowed statistical deviations D. M. Webber16

17. Final Errors and Numbers ppm units  (R06) = 2 196 979.9 ± 2.5 ± 0.9 ps  (R07) = 2 196 981.2 ± 3.7 ± 0.9 ps  (Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps

18. Results The Result  (R06) = 2 196 979.9 ± 2.5 ± 0.9 ps  (R07) = 2 196 981.2 ± 3.7 ± 0.9 ps  (Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps New G F G F (MuLan) = 1.166 378 8(7) x 10 -5 GeV -2 (0.6 ppm)

19. 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

20. In hydrogen:   - )-(1/   + ) =  S  g P now in even better agreement with ChPT * * Chiral Perturbation Theory Using previous   world average 20 Shifts the MuCap result Using new MuLan   average

21. MuLan Collaborators 2007 2006 2004 21D. 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

22. 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 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) = 2 196 979.9 ± 2.5 ± 0.9 ps  (R07) = 2 196 981.2 ± 3.7 ± 0.9 ps  (Combined) = 2 196 980.3 ± 2.2 ps (1.0 ppm)  (R07 – R06) = 1.3 ps G F (MuLan) = 1.166 378 8(7) x 10 -5 GeV -2 (0.6 ppm)

23. Backup D. M. Webber23

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

25. Gain is photomultiplier tube type dependent D. M. Webber25 Deviation at t=0 Artifact from start signal 0 10 20  s 1 ADC = 0.004 V Sag in tube response

26. pileup Introducing higher-order pileup D. M. Webber26 hit time Artificial deadtime hit time Artificial deadtime Inner tile Outer tile Artificial deadtime triple ABCDEFG

27. 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 –Both @ 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 !!