1. Measuring muon decay with TWIST Glen Marshall, for the TWIST Collaboration CIPANP06, Puerto Rico

2. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 2 The T RIUMF W eak I nteraction S ymmetry T est  Tests Standard Model predictions for muon decay.  Uses highly polarized  + beam.  Stops  + in a very symmetric detector.  Tracks e + through uniform, well-known field.  Extracts decay parameters by comparison to detailed and verified simulation.

3. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 3 Michel parameter description  Muon decay (Michel) parameters , , P  ,   muon differential decay rate vs. energy and angle:  where  and Louis Michel  pepe PP

4. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 4 Pre- TWIST decay parameters  From the Review of Particle Physics (SM values in parentheses) :   = 0.7518 § 0.0026 (Derenzo, 1969) (0.75)   = -0.007 § 0.013 (Burkard et al., 1985) (0.00)   = 0.7486 § 0.0026 § 0.0028 (Balke et al., 1988) (0.75)  P   = 1.0027 § 0.0079 § 0.0030 (Beltrami et al., 1987) (1.00)  P  (  /  ) > 0.99682 (Jodidio et al., 1986) (1.00) The goal of TWIST is to find any new physics which may become apparent by improving the precision of each of , , and P   by at least one order of magnitude compared to prior experimental results.

5. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 5 Michel shape, graphically Full O(  ) radiative corrections with exact electron mass dependence. Leading and next-to-leading logarithmic terms of O(  2 ). Leading logarithmic terms of O(  3 ). Corrections for soft pairs, virtual pairs, and an ad-hoc exponentiation. Arbuzov et al., Phys. Rev. D66 (2002) 93003. Arbuzov et al., Phys. Rev. D65 (2002) 113006.

6. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 6 Michel parameters and coupling constants  Fetscher and Gerber coupling constants (see PDG):

7. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 7 Coupling constants  Coupling constants g   can be related to handedness, e.g., total muon right-handed coupling:  Global analysis of  decay (Gagliardi et al., PRD 72 2005)  no existing similar analysis for other weak decays.  Neutrino mass implications at 10 -7 -10 -4 for LR/RL:  J. Kile (CIPANP06), Erwin et al. (hep-ph/0602240)

8. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 8 Fitting the data distributions  Michel distribution is linear in , , P  , and P  , so a fit to first order expansion is exact.  Fit data to simulated (MC) base distribution with hidden assumed parameters, MC = ( , , P   | P  , P   ) plus MC-generated distributions from analytic derivatives, times fitting parameters (  ) representing deviations from base MC. (graphic thanks to Blair Jamieson)

9. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 9 Evaluation of Systematic Uncertainties  TWIST relies on a fit to simulation:  Simulation must be verified.  Reconstruction systematics eliminated if simulation is perfect.  General method:  exaggerate a condition (in data or MC) which may cause error.  measure effect by fitting, using correlated sets where practical.  scale results according to variance in a data set.  Linearity? Double counting? Positron interactions: Energy smearing Multiple scattering Hard interactions Material in detector Material outside Chamber response: DC and PC efficiencies Dead zone Long drift times HV variations Temperature, pressure Chamber foil bulges Crosstalk Variation of t 0 Momentum calibration: End point fits Field reproduction Muon beam stability: Stopping location Beam intensity Magnet stability Spectrometer alignment: Translations Rotations Longitudinal Field to detector axis

10. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 10 Fits to data distributions Above: normalized residuals of fit, and fiducial region used for fit: p < 50 MeV/c, 0.50 < |cos  | < 0.84, |p z | > 13.7 MeV/c, p T < 38.5 MeV/c. Left: comparison of data to fit (MC) vs. momentum, also showing (MC reconstructed)/(MC thrown) comparisons and normalized residuals.

11. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 11 Fits to data distributions (cont.) Angular distributions for restricted momentum ranges. Dashed lines show fiducial region of two-dimensional fit. Dependence of asymmetry on momentum, its two contributions, and comparison of data and fit (MC)distributions.

12. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 12 Summary of results:  and    = 0.75080 § 0.00044(stat) § 0.00093(syst) § 0.00023(  )  2.5 times better precision than PDG value.  Uncertainty scaled for  2 /dof = 7.5/4 (CL=0.11) for different data sets.  J.R. Musser et al., PRL 94, 101805 (2005), hep-ex/0409063.   = 0.74964 § 0.00066(stat) § 0.00112(syst)  2.9 times better precision than PDG value.  A. Gaponeko et al., PRD 71, 071101(R) (2005), hep-ex/0410045.  Using the above values of  and , with P  (  /  ) > 0.99682 (PDG) and Q R  ¸ 0, we get 0.9960 < P   ·  < 1.0040 (90% c.l.)  improves upon P   = 1.0027 § 0.0079 § 0.0030.

13. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 13 Systematic uncertainties:  and  Systematic uncertainties  ( £ 10 4 )  ( £ 10 4 ) publishedcurrentpublishedcurrent Chamber response (ave)5.10.15.61.5 Stopping target thickness4.9-3.7- Positron interactions4.63.65.56.5 Spectrometer alignment2.20.46.1- Momentum calibration (ave)2.01.12.92.2 Theoretical radiative correction2.0 1.0 Muon beam stability (ave)0.40.51.00.9 Track selection algorithm1.1- Asymmetric efficiencies0.40.1 Total in quadrature9.34.311.27.2 New data and analysis: thesis of R.P. MacDonald, in preparation.

14. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 14 Summary of results: P    P   = 1.0003 § 0.0006(stat) § 0.0038(syst)  2.2 times better precision than PDG value (Beltrami et al.).  still not as precise as TWIST indirect result from  and .  B. Jamieson et al., recently submitted to PRD, hep-ex/0605100.  Dominated by systematic uncertainty from spectrometer fringe field depolarization:  prospects for improvement are excellent.  data was taken in 2004; new data with improved muon beam will be taken in 2006-07.

15. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 15 Systematic uncertainties: P   Systematic uncertainties P   ( £ 10 3 ) Depolarization in fringe field (ave)3.4 Depolarization in muon stopping material (ave)1.2 Chamber response (ave)1.0 Spectrometer alignment0.3 Positron interactions (ave)0.3 Depolarization in muon production target0.2 Momentum calibration0.2 Upstream-downstream efficiency0.2 Background muon contamination (ave)0.2 Beam intensity (ave)0.2 Michel  parameter 0.1 Theoretical radiative correction0.1 Total in quadrature3.8

16. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 16 Fringe field systematic improvement The TECs (time expansion chambers) are transverse drift chambers operating at 0.08 bar, separated from beam vacuum by 6  m Mylar windows. Two modules measure x and y.

17. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 17 Left-right symmetric models  Weak eigenstates in terms of mass eigenstates and mixing angle:  Assume possible differences in left and right couplings and CKM character. Use notation:  Then, for muon decay, the Michel parameters are modified:  “manifest” LRS assumes g R = g L, V R = V L,  = 0 (no CP violation).  “pseudo-manifest” LRS allows CP violation, but V R = ( V L )* and g R = g L.  RS “non-manifest” or generalized LRS makes no such assumptions.  Most experiments must make assumptions about LRS models!

18. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 18 Limits on LRS parameters: PDG04 Observablem 2 (GeV/c 2 )  +- m(K L – K S )>1600reach(P)MLRS Direct W R searches >720-650 (D0) >652 (CDF) clear signal (P)MLRS decay model CKM unitarity <10 -3 sensitivity (P)MLRS heavy R  decay >310<0.040 both parameters (P)MLRS light R  decay ( TWIST ) >406 (>420) <0.033 (<0.030) model independence light R

19. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 19 Muon decay LRS limits Restricted (“manifest”) LRS modelGeneral LRS model Exclusion (90% cl) plots for left-right symmetric model mixing angle and right partner boson W 2 mass m 2

20. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 20 Summary  TWIST has produced its first direct measurement of P  , to add to previous results for  and .  Analysis underway for second measurements for  and , representing further improvements by » 2.  Reduction of depolarization systematics for P   seems achievable, but it is not yet known by how much.  In 2006-2008, TWIST will produce its final results:  goal remains the reduction of uncertainty by an order of magnitude compared to previous muon decay parameter experiments 

21. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 21 TWIST Participants TRIUMF Ryan Bayes ¤y Yuri Davydov Jaap Doornbos Wayne Faszer Makoto Fujiwara David Gill Peter Gumplinger Anthony Hillairet ¤y Robert Henderson Jingliang Hu John A. Macdonald x Glen Marshall Dick Mischke Mina Nozar Konstantin Olchanski Art Olin y Robert Openshaw Tracy Porcelli z Jean-Michel Poutissou Renée Poutissou Grant Sheffer Bill Shin zz Alberta Andrei Gaponenko ¤¤ Peter Kitching Robert MacDonald ¤ Maher Quraan y Nate Rodning x John Schaapman Glen Stinson British Columbia James Bueno ¤ Mike Hasinoff Blair Jamieson ¤¤ Montréal Pierre Depommier Regina Ted Mathie Roman Tacik Kurchatov Institute Vladimir Selivanov Vladimir Torokhov Texas A&M Carl Gagliardi Jim Musser ¤¤ Bob Tribble Maxim Vasiliev Valparaiso Don Koetke Paul Nord Shirvel Stanislaus ¤ Graduate student ¤¤ Graduated y also U Vic z also Manitoba zz also Saskatchewan x deceased Supported under grants from NSERC (Canada) and DOE (USA). Computing facilities of WestGrid are gratefully acknowledged.

22. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 22 Questions? Comments? Requests to work on TWIST as a post-doc?

23. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 23 Outline  Muons and muon decay  What is a muon?  Some history of the weak interaction  Details of muon decay  The TWIST experiment  Muon beam production  Spectrometer  Analysis methods  Results obtained and anticipated  Systematic uncertainties  TWIST values for muon decay parameters  Consequences of results obtained so far  How much better can we do?

24. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 24 Properties of muons  Muons (  -,  + ):  are leptons.  are not affected by strong interactions (great for weak interaction tests!)  Mass:  105.658369(9) MeV/c 2  200 £ m e, 1/9 £ m p  Lifetime:  2.19703(4)  s  Decay:  99%  E e max = 52.8 MeV  Spin:  ½  easily produced with high polarization.  a  ´ (g  – 2)/2 = 11 659 208 (6) £ 10 -10 (0.5 ppm)

25. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 25 Muon decay made simple  Assume four-fermion interaction which is:  Lorentz invariant  local  lepton-number-conserving  Allows scalar, vector, or tensor; left or right; or combinations.

26. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 26 The Fermi theory   decay - analogy with electrodynamics (Dirac et al.,) but generalizing also to scalar and tensor interactions (1934-36):  Originally parity-conserving, but modified after suggestions of Lee and Yang (1956), and observations of Wu et al. (  decay) and Garwin, Friedman and Telegdi (  decay) (1957).  Low energy description (“V-A”) for Standard Model of particle physics. But how valid is V-A? E. Fermi C.S. Wu

27. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 27  Description of Fetscher and Gerber (see PDG Review):  Includes includes scalar, vector, and tensor (  S,  V,  T ) interactions among left- and right-handed , e.  Probability for decay of  –handed muon to  –handed electron is easily expressed: Matrix elements

28. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 28 New calculations from masses Coupling Constant Global Analysis from  mass limits | g LR S | <0.0884 £ 10 -7 | g LR T | <0.0252 £ 10 -7 | g RL S | <0.4178 £ 10 -5 | g RL T | <0.1044 £ 10 -5 | g LR V | <0.0368 £ 10 -7 | g RL V | <0.1042 £ 10 -4  Erwin et al., hep-ph/0602240  comparison to Gagliardi et al.  consider operators that contribute to both processes (no LL, RR)  motivated by TWIST results

29. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 29 Testing the Standard Model  Model independent muon handedness:  Left-right symmetric models (simplified!):  Tensor interaction (M. Chizhov, hep-ph/0405073):

30. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 30 Surface muon beam  Pions decaying at rest produce muon beams with P  > 99%.  Depolarization must be controlled using small beams near kinematic edge, 29.8 MeV/c.  Use » 2.5 £ 10 3  + s -1.  Muon total range at density » 1 only about 1.5 mm! M13 beam line

31. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 31 Types of muon beams Decay beam Cloud beam Surface  + beam Surface muons have high polarization (in the direction of muon momentum) and high luminosity at low momentum (<29.79 MeV/c, or 4.1 MeV).

32. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 32 Muon TOF and polarization Time of flight with respect to accelerator RF (43 ns period). Pion decay at rest leads to 26 ns exponential for surface muon arrival time, while low polarization cloud muons are at the leading edge of surface muon time distribution. high polarization cloud muon contamination

33. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 33 Solenoid field  20 year old ex-MRI superconducting solenoid provides 2 T field.  Steel yoke improves uniformity, reduces stray fields.  Uniform to 4 £ 10 -3, mapped to precision of 5 £ 10 -5.

34. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 34 Detector array  56 low-mass high-precision planar chambers symmetrically placed around thin target foil which stops nearly all of surface muon beam.  Measurement initiated by single thin scintillation counter at entrance to detector.  Beam stop position controlled by variable He/CO 2 gas degrader.

35. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 35 Support cradle Array of 56 detector planes in the support cradle

36. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 36 Data distributions Acceptance of TWIST spectrometer e energy loss / 1/cos 

37. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 37 Blind analysis motivation  Reduce “human” systematics, i.e., biases.  Keep final result hidden until analysis is completed and systematic uncertainties evaluated.  In fit procedure, the set of simulation parameters MC is encrypted and unknown; results of fits are differences  from hidden values. A. Gaponenko, Ph.D. thesis

38. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 38 First TWIST analysis  Data taken in Fall 2002:  6 £ 10 9 muon decay events in data sets of about 3 £ 10 8 events (2-3 days) each.  Five (  ) or four (  ) sets were analyzed and fit to extract results.  Remainder were for systematic tests.  Analysis relied on WestGrid installation at UBC:  1040 ( ! 1680) Intel 3 GHz processors in total.  Was available in late 2003; operating well in early 2004.  TWIST used » 31,000 processor days in 2004 to analyze data and simulations.

39. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 39 Systematics: positron interactions  GEANT simulation must be validated for e + energy loss and multiple scattering.  Stop muons at one end of detector.  Measure e + track on each side of target, before and after passage through it.  Compare differences, with data and MC. modified  +  stop position DS UStarget

40. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 40 Revealing the hidden parameters  The base set is generated using unknown, hidden values of ( MC ).  All systematic uncertainties as well as offsets  are confirmed prior to revealing hidden values.

41. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 41 The next step... “Do you by any chance have the real TWIST disk?” “Yes!”

42. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 42 Results of different data sets Data set  (stat)(syst)  2 dof=1887  (stat)(syst)  2 dof=1887 Set A0.75134(83)(53)18140.75087(156)(73)1924 Set B0.74937(66)(53)19650.74979(124)(55)1880 1.96 T0.75027(65)(55)19510.74918(124)(69)1987 2.04 T0.75248(70)(60)18040.74908(132)(65)1947 Cloud  + 0.75157(76)(53)1993--

43. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 43 Handedness of the muon Diagonal represents exactly left-handed muon decay. Shaded regions represent comparison of current (indirect) and proposed (direct) TWIST limits, compared to previous PDG limits.

44. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 44 What’s new? Systematics for P   Systematic uncertaintiescontributions P   ( £ 10 3 ) preliminary Muon beam and polarization3.69 Fringe field (ave)3.40 Stopping target (ave)1.40 Production target0.21 Chamber response0.98 Positron interactions0.32 Spectrometer alignment0.31 Momentum calibration0.19 Total in quadrature3.8 (see Blair Jamieson, Ph.D thesis, UBC, nearly complete)

45. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 45 Next Steps  Complete first direct TWIST P   measurement:  final checks of depolarization systematic nearly complete.  reveal blind parameters: open the box.  week(s) away (B. Jamieson thesis).  Complete second round for  and  :  some improvements to analysis in progress.  new set of blind parameters.  early 2006 (R.P. MacDonald thesis, UofA).  Work hard on systematic improvements  especially P  .

46. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 46 Momentum dependence of F IS Momentum dependence of isotropic part of muon decay spectrum (black), compared with magnified (300x) contribution of  (red) and  (blue) at PDG limits.

47. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 47 Analysis Methods  Extract energy and angle distributions for data:  apply (unbiased) cuts on muon variables.  reject fast decays and backgrounds.  calibrate e + energy to kinematic end point at 52.8 MeV.  Fit to identically derived distributions from simulation:  GEANT3 geometry contains virtually all detector components.  simulate detector response in detail (clusters of ionization).  realistic, measured beam profile and divergence.  extra muon and beam positron contamination included.  output into digitized format, identical to real data.  fit to hidden variables with blind analysis method.

48. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 48 Analysis of data and simulation  Read out chamber hits in time interval [-6,+10]  s.  Use pattern recognition (in position and time) to sort hits into tracks, then fit to helix.  Write track parameters and other variables.  Must recognize beam positrons, delta tracks, backscattering tracks.

49. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 49 Energy calibration  Use only distinctive feature of distribution: the end point.  Fit edge energy and width for narrow angle ranges.  Edge energy: absolute and angle- dependent parameters , .  With correct field,  = 0.   represents energy loss, mostly in muon stopping target.

50. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 50 Systematics: two examples  Muon stopping target was 125  m Mylar, coated with 10 § 10  m graphite for conductivity. What is uncertainty in decay parameters due to the thickness uncertainty?  simulate with 30  m graphite thickness (2 £ exaggeration).  fit to simulation (correlated!) with nominal thickness: shift for  of -0.98 £ 10 -3 and  of -0.73 £ 10 -3.  divide shift by exaggeration factor.  HV was maintained to accuracy of § 5 V. What is uncertainty in decay parameters due to HV variation?  take data set with HV lowered by 100 V (20 £ exaggeration).  fit to nominal (uncorrelated) data set: shift for  of -0.70 £ 10 -3 and  of +0.08 £ 10 -3.  divide shift by exaggeration factor.

51. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 51 Simulation: muon interactions  Simulation must reliably predict muon stopping distributions.  Verify by comparison in low-mass detector region. stop region Data Simulation

52. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 52 Systematics: e + hard scattering (MC reconstructed)/(MC simulated) vs. p for  p < 1 MeV/c (“intermediate”) (MC reconstructed)/(MC simulated) vs. p for  p > 1 MeV/c (“hard”) Estimate change in yield for intermediate (0.30%) and hard (0.37%) interactions over fiducial volume. Calculate influence on  and . Scale according to GEANT3 simulation verification: 5% for intermediate and 14% for hard scattering interactions.

53. CIPANP06, June 1, 2006 G.M. Marshall, Muon decay with TWIST 53 Are there derivative couplings?   radiative decay experiments see a small anomaly which might be explained by a tensor interaction. (hep-ex/0312029, recently published in Phys. Rev. Lett.)  Chizhov (hep-ph/0405073) calculates:   = ¾(1 – 6| g T RR | 2 ) ¼ 0.74924  deviation from Standard Model value is » 2 £ less than current TWIST precision.