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 POSITIVE MUON LIFETIME AND DETERMINATION OF THE FERMI CONSTANT

2. Outline Motivation Experiment Hardware Analysis –Pulse Fitting –Fit Results Systematic Uncertainties –Gain Stability –Pileup –Spin Rotation Final Results D. M. Webber2

3. Motivation gives the Fermi Constant to unprecedented precision (actually G  ) needed for “reference” lifetime for precision muon capture experiments –MuCap –MuSun Capture rate from lifetime difference    and  

4. 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

5. 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 5D. 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)

6. D. M. Webber6

7. 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 G F determinations –Both published intermediate results on small data samples n Meanwhile, more theory updates !!

8. 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

9. 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

10. Experiment D. M. Webber10

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

12. The beamline transports ~10 7 “surface” muons per second to the experimental area. Momentum Selection Parallel beam Velocity separator removes beam positrons Spatial focus

13. A kicker is used to create the time structure. 22  s 5  s Extinction ~ 1000 Trigger Suppression Accumulation Period Measuring Period kicker counts arb.

14. ARNOKROME™ III (AK-3) high-field target used in 2006 - Rapid precession of muon spin - mSR studies show fast damping

15. The target was opened once per day to view the beam profile. D. M. Webber15 Target rotates out of beam

16. 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  s accumulation period Muons precess by 0 to 350 revolutions 16D. M. Webber

17. 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

18. 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)

19. Each section contains either 6 or 5 tile elements a Each element is made from two independent scintillator tiles with light guides and photomultiplier tubes. The detector is composed of 20 hexagon and 10 pentagon sections, forming a truncated icosahedron.

20. 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 20D. M. Webber Uncertainty on lifetime from gain stability: 0.25 ppm x2

21. 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

22. MuLan collected two datasets, each containing 10 12 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, 2006Quartz Target, 2007

23. Analysis D. M. Webber23

24. Fits of raw waveforms using Templates A difficult fit Normal Pulse Two pulses close together >2 x 10 12 / data set 225 TBytes data at NCSA

25. 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 25D. M. Webber Two pulses close together A difficult fit inner outer ADT Template

26. Nearby pulses perturb the time of main pulses. Studied with simulations D. M. Webber26 Fixed reference perturbation  t avg Estimated pull:

27. 2006: Fit of 30,000 AK-3 pileup-corrected runs. 22  s ppm   +  secret R vs fit start time Red band is the set-subset allowed variance Relative  (ppm) 0 9  s

28. 2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The  SR remnants vanish.

29. Systematics Introduction D. M. Webber29

30. Leading systematic considerations: Challenging

31. Systematics: Gain Stability D. M. Webber31

32. Gain is photomultiplier tube type dependent D. M. Webber32 Deviation at t=0 Artifact from start signal 0 10 20  s 1 ADC = 0.004 V Sag in tube response

33. Gain variation vs. time is derived from the stability of the peak (MPV) of the fit to pulse distribution 33 0 10 20  s 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.

34. Systematics: Pileup D. M. Webber34

35. 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

36. pileup Introducing higher-order pileup D. M. Webber36 hit time Artificial deadtime hit time Artificial deadtime Inner tile Outer tile Artificial deadtime triple ABCDEFG

37. 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

38. The pileup corrections were tested with Monte-Carlo. D. M. Webber38 Monte-Carlo Simulation, 10 12 events agrees with truth to < 0.2 ppm 1.19 ppm statistical uncertainty

39. 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. Webber Pileup Correction Uncertainty: 0.2 ppm

40. 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. Webber40

41. Systematics Spin Precession D. M. Webber41

42. 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+e+  The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates. E e = E max = 52.83 MeV Positron energy distribution E e = 26.4 MeV E e = 13.2 MeV Detection threshold Highest Energy Positrons Lowest Energy Positrons

43.  SR rotation results in an oscillation of the measurement probability for a given detector. B = 34 GB = 1 G This oscillation is easily detected This oscillation is not easily detected and systematic errors may arise B   counts arb.

44.  SR relaxation results in a reduction of the polarization magnitude. T1 is independent of magnetic field.T2 is from an inhomogeneous field.

45. The sum cancels muSR effects; the difference accentuates the effect. SumDifference/Sum B   counts arb.

46. 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

47. 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

48. 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

49. 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

50. 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)

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

52. 2007: Consistency against MANY special runs, where we varied target, magnet, ball position, etc. Start-time scan

53. Consistency Checks D. M. Webber53

54. 2006: Fit of 30,000 AK-3 pileup-corrected runs 22  s ppm   +  secret R vs fit start time Red band is the set-subset allowed variance Relative  (ppm) 0 9  s

55. 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

56. 2007: Quartz data fits well as a simple sum, exploiting the symmetry of the detector. The  SR remnants vanish

57. Variations in    vs. fit start time are within allowed statisical deviations D. M. Webber57

58. Conclusions D. M. Webber58

59. 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

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

61. Lifetime “history” New G F G F (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

62. 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 The Result

63. 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

64. In hydrogen:   - )-(1/   + ) =  S  g P now in even better agreement with ChPT * * Chiral Perturbation Theory Using previous   world average 64 Shifts the MuCap result Using new MuLan   average

65. 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 g P to better agreement with theory –“Eliminates” the error from the positive muon lifetime, needed in future MuCap and MuSun capture determinations  (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

66. MuLan Collaborators 2007 2006 2004 66D. 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

67. D. M. Webber67

68. Backup Slides

69. What is g P ? g P is the pseudoscalar form factor of the proton 69D. M. Webber

70. 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

71. 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 71D. M. Webber

72. Miscellaneous D. M. Webber72

73. 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+e+  The decay positron energy and angular distributions are not uniform, resulting in position dependant measurement rates. E e = E max = 52.83 MeV Positron energy distribution E e = 26.4 MeV E e = 13.2 MeV Detection threshold Highest Energy Positrons Lowest Energy Positrons

74. Effect of  on G F In the Standard Model,  =0, General form of  Drop second-order nonstandard couplings Effect on G F return 74D. M. Webber