1. 1 A 1 ppm measurement of the positive muon lifetime Qinzeng Peng Advisor: Robert Carey Boston University October 28, 2010 MuLan collaboration at BU: Robert Carey, James Miller, Lee Roberts, Kevin Lynch, Justin Phllips, William Earle Institutes: BU, UIUC, Univ. of Kentucky, JMU

2. 2 Outline I. Motivation and theory II. MuLan experimental set up III. 2006 data analysis IV. Systematic errors V. Final results

3. 3 Input parameters to the standard model and their precision measurements The CKM mixing matrix The CKM mixing matrix The masses of fermions and Higgs boson The masses of fermions and Higgs boson 3 parameters to determine the strength of the interaction and the masses of the weak gauge bosons 3 parameters to determine the strength of the interaction and the masses of the weak gauge bosons Fine structure constant α Fine structure constant α Z-boson mass M Z Z-boson mass M Z Fermi constant G F Fermi constant G F 0.71 ppb 23 ppm 8.6 ppm MuLan

4. 4 Fermi Constant and g Contains all weak interaction loop corrections

5. 5 Fermi Constant and τ μ Radiative corrections (maily QEC) Contact interaction from Fermi theory In 1999, van Ritbergen and Stuart completed full 2-loop QED corrections reducing the uncertainty in GF from theory to < 0.3 ppm (it was the dominant error before)

6. 6 A Graphical History of the Muon Lifetime Measurements

7. 7 Experimental Concept Traditional method: 1 muon decay each time MuLan method: n muons decay each cycle need pulsed muon beam  kicker -12.5 kV +12.5 kV Accumulation period Measurement period

8. 8 Experimental Setup beam line kicker detector ball WFD DAQ monitoring devices

9. 9 Kicker 2 sets of parallel plates inside the vacuum pipe high voltage at +/- 12.5 KeV fast transition time (60 ns)

10. 10 Target Ferromagnetic target to dephase muons’ polarization during accumulation period. Polarization is both depolarized and dephased. Ferromagnetic target to dephase muons’ polarization during accumulation period. Polarization is both depolarized and dephased. Arnokrome-3 (AK3) Target (~28% chromium, ~8% cobalt, ~64% iron) 0.5 T internal magnetic field Muons arrive randomly during 5 us accumulation period Muons precess by 0 to 350 revolutions

11. 11 Muon Corridor Errant muons => vacuum pipe Errant muons => vacuum pipe AK-3 Target inside the pipe AK-3 Target inside the pipe AK3 liner AK3 liner

12. 12 Entrance Muon Counter to monitor beam profile Target rotates out of beam

13. 13 MuLan Detector Ball 170 detector pairs = 20 hexagons + 12 pentagons 170 detector pairs = 20 hexagons + 12 pentagons

14. 14 Detector elements

15. 15 Waveform digitizer 2 Analog Pulses WFD 1 WFD 2 Anlog signal => Digitized samples ( ampitude and time)

16. 16 More than 10 12 muon decays in 2006 run >1 x 10 12 coincidence pulses in 2006 data set >65 TBytes raw data

17. 17 Data analysis 3-parameter fit 3-parameter fit 4-parameter fit 4-parameter fit Artificial pile-up construction Artificial pile-up construction

18. 18 Systematic studies Early to late stability during 22 μs measuring period Early to late stability during 22 μs measuring period Kicker stability Kicker stability Background stability Background stability Timing stability Timing stability Gain stability Gain stability

19. 19 Timing stability – with laser system Need reference time, Need reference time, Laser pulse is narrower than normal pulse Laser pulse is narrower than normal pulse Reference PMT is NOT contaminated with experimental background Reference PMT is NOT contaminated with experimental background

20. 20 Laser system setup

21. 21 Laser runs 24 tile laser channels 24 tile laser channels 3305 laser runs in 2006 => 5E6 hits per channel 3305 laser runs in 2006 => 5E6 hits per channel Combine the runs to study dt vs. time => 1.6E6 hits needed for 0.5 ppm error. Combine the runs to study dt vs. time => 1.6E6 hits needed for 0.5 ppm error.

22. 22 dt vs. run stability the scale of change is about 0.02 clock ticks In single run sigma of dt=0.13 clock ticks (in next slide)

23. 23 Multi peaks combination

24. 24 dT vs. time, single channel

25. 25 dT vs. time, 24 channels Mean = -5E-9 c.t. per clock tick is close to 0 RMS = 6E-8 c.t. per clock tick as the timing shift Timing shift error: 0.06 ppm c.t per c.t.

26. 26 Timing stability Timing is pretty stable for MuLan experiment, at 0.1 ppm level Timing is pretty stable for MuLan experiment, at 0.1 ppm level

27. 27 Gain stability Gain shift == threshold shift Gain shift == threshold shift Gain shift => number vs. time shift Gain shift => number vs. time shift vs. time is studied

28. 28 Gain shift to lifetime shift

29. 29 Run selection big fluctuation from run 33282 to 54318(index 1 to 225) slight change (10 ADC) from run 54330 to 55428 (index 225 to 400) Sigma of amplitude of single run is 10 -15 ADC Better region

30. 30 Ratio method Ratio of amplitude of tile pulse to amplitude of the reference PMT Ratio of amplitude of tile pulse to amplitude of the reference PMT Ratio of amplitude of time bin I to amplitude of the last time bin Ratio of amplitude of time bin I to amplitude of the last time bin

31. 31 d(amp)/amp = (108-98)/98=0.1 d(amp_ratio)/amp_ratio = (0.68-0.655)/0.655 = 0.0382

32. 32 Slope of ratio_bin_i vs. run – flat distribution

33. 33 vs. time vs. time

34. 34 24 channels combined d(dG/G)/dt = 5E-5 per tau

35. 35 Counts shift due to threshold change dN/N ≈ 3 x 10 -4 for 1 ADC change in threshold

36. 36 conclusion Amp vs. time < 1 ppm Amp vs. time < 1 ppm

37. 37 WFD Pulse Fitter Algorithm

38. 38 Foucs on neighboring pulses

39. 39 Test of PFA Pile on effect, signal region and pedestal region Pile on effect, signal region and pedestal region

40. 40 Effect of small pile on

41. 41 Effect of pile on near threshold

42. 42 Change vs. amplitude of pile on

43. 43 Estimated pull of timing

44. 44 MuSR effect MuSR rotation results in an oscillation of the measurement probability for a given detector. B   B = 34 G

45. 45 MuSR relaxation results in a reduction of the polarization magnitude.

46. 46 The sum cancels muSR effects the difference accentuates the effect. SumDifference/Sum B   counts arb.

47. 47 conclusions Timing shift => 0.1 ppm Timing shift => 0.1 ppm Gain shift => < 1 ppm PFA => < 0.1 ppm