1. B. Lee Roberts, Oxford University, 19 October 2004 - p. 1/55 The Muon: A Laboratory for Particle Physics Everything you always wanted to know about the muon but were afraid to ask. B. Lee Roberts Department of Physics Boston University roberts@bu.eduroberts@bu.edu http://physics.bu.edu/roberts.html

2. B. Lee Roberts, Oxford University, 19 October 2004 - p. 2/55 Outline Introduction to the muon Selected weak interaction parameters Muonium Lepton Flavor Violation Magnetic and electric dipole moments Summary and conclusions.

3. B. Lee Roberts, Oxford University, 19 October 2004 - p. 3/55 The Muon (“Who ordered that?”) Lifetime ~2.2  s, practically forever 2 nd generation lepton m   m e = 206.768 277(24) produced polarized For decay in flight, “forward” and “backward” muons are highly polarized.

4. B. Lee Roberts, Oxford University, 19 October 2004 - p. 4/55 The Muon – ctd. Decay is self analyzing It can be produced copiously in pion decay –PSI has 10 8  /s in a new beam

5. B. Lee Roberts, Oxford University, 19 October 2004 - p. 5/55 A precise measurement of   + leads to a precise determination of G F Predictive power in weak sector of SM: Top quark mass prediction:m t = 177  20 GeV Input: G F (17 ppm),  (4 ppb at q 2 =0), M Z (23 ppm), 2004 Update from D0m t = 178  4.3 GeV

6. B. Lee Roberts, Oxford University, 19 October 2004 - p. 6/55  Lan @ PSI aims for a factor of 20 improvement

7. B. Lee Roberts, Oxford University, 19 October 2004 - p. 7/55 The Leptonic Currents Lepton current is (V – A) There have been extensive studies at PSI by Gerber, Fetscher, et al. to look for other couplings in muon decay.

8. B. Lee Roberts, Oxford University, 19 October 2004 - p. 8/55 Leptonic and hadronic currents For nuclear   capture there are induced formfactors and the hadronic current contains 6 terms. –the induced pseudoscaler term is important further enhanced in radiative muon capture A new experiment at PSI MuCap hopes to resolve the present 3  discrepancy with PCAC

9. B. Lee Roberts, Oxford University, 19 October 2004 - p. 9/55 Muonium Hydrogen (without the proton) Zeeman splitting    p = 3.183 345 24(37) (120 ppb) where  p comes from proton NMR in the same B field

10. B. Lee Roberts, Oxford University, 19 October 2004 - p. 10/55 muonium and hydrogen hfs → proton structure

11. B. Lee Roberts, Oxford University, 19 October 2004 - p. 11/55 Lepton Flavor We have found empirically that lepton number is conserved in muon decay and in beta decay. –e.g. What about or

12. B. Lee Roberts, Oxford University, 19 October 2004 - p. 12/55 General Statements We know that oscillate –neutral lepton flavor violation Expect charged lepton flavor violation at some level –enhanced if there is new dynamics at the TeV scale in particular if there is SUSY We expect CP in the lepton sector (EDMs as well as oscillations) –possible connection with cosmology (leptogenesis)

13. B. Lee Roberts, Oxford University, 19 October 2004 - p. 13/55 The Muon Trio: Lepton Flavor Violation Muon MDM (g-2) chiral changing Muon EDM

14. B. Lee Roberts, Oxford University, 19 October 2004 - p. 14/55 Past and Future of LFV Limits +e-→-e++e-→-e+ MEG  → e  –10 -13 BR sensitivity under construction at PSI, first data in 2006 MECO  + +A→e + +A –10 -17 BR sensitivity approved at Brookhaven, not yet funded (Needs Congressional approval) Branching Ratio Limit

15. B. Lee Roberts, Oxford University, 19 October 2004 - p. 15/55 Magnetic Dipole Moments The field was started by Stern

16. B. Lee Roberts, Oxford University, 19 October 2004 - p. 16/55 Z. Phys. 7, 249 (1921)

17. B. Lee Roberts, Oxford University, 19 October 2004 - p. 17/55 (in modern language) 673 (1924)

18. B. Lee Roberts, Oxford University, 19 October 2004 - p. 18/55 Dirac + Pauli moment

19. B. Lee Roberts, Oxford University, 19 October 2004 - p. 19/55 Dirac Equation Predicts g=2 radiative corrections change g

20. B. Lee Roberts, Oxford University, 19 October 2004 - p. 20/55 The CERN Muon (g-2) Experiments The muon was shown to be a point particle obeying QED The final CERN precision was 7.3 ppm

21. B. Lee Roberts, Oxford University, 19 October 2004 - p. 21/55 Standard Model Value for (g-2) relative contribution of heavier things

22. B. Lee Roberts, Oxford University, 19 October 2004 - p. 22/55 Two Hadronic Issues: Lowest order hadronic contribution Hadronic light-by-light

23. B. Lee Roberts, Oxford University, 19 October 2004 - p. 23/55 Lowest Order Hadronic from e + e - annihilation

24. B. Lee Roberts, Oxford University, 19 October 2004 - p. 24/55 a(had) from hadronic  decay? Assume: CVC, no 2 nd -class currents, isospin breaking corrections. n.b.  decay has no isoscalar piece, while e + e - does Many inconsistencies in comparison of e + e - and  decay: - Using CVC to predict  branching ratios gives 0.7 to 3.6  discrepancies with reality. - F  from  decay has different shape from e + e -.

25. B. Lee Roberts, Oxford University, 19 October 2004 - p. 25/55 Comparison with CMD-2 in the Energy Range 0.37 < s p <0.93 GeV 2 (375.6  0.8 stat  4.9 syst+theo ) 10 -10 (378.6  2.7 stat  2.3 syst+theo ) 10 -10 KLOE CMD2 1.3 % Error 0.9 % Error a   = ( 388.7  0.8 stat  3.5 syst  3.5 theo ) 10 -10 2 p contribution to a m hadr KLOE has evaluated the Dispersions Integral for the 2-Pion-Channel in the Energy Range 0.35 < s p <0.95 GeV 2 At large values of s  (>m   ) KLOE is consistent with CMD and therefore They confirm the deviation from t -data!. Pion Formfactor CMD-2 KLOE 0.40.50.60.70.80.9 s  [GeV 2 ] 45 40 35 30 25 20 15 10 5 45 0 KLOE Data on R(s) Courtesy of G. Venanzone

26. B. Lee Roberts, Oxford University, 19 October 2004 - p. 26/55 A. Höcker at ICHEP04

27. B. Lee Roberts, Oxford University, 19 October 2004 - p. 27/55 a  had [e + e – ] = (693.4 ± 5.3 ± 3.5)  10 –10 a  SM [e + e – ] = (11 659 182.8 ± 6.3 had ± 3.5 LBL ± 0.3 QED+EW )  10 –10 Weak contribution a  weak = + (15.4 ± 0.3)  10 –10 Hadronic contribution from higher order : a  had [(  /  ) 3 ] = – (10.0 ± 0.6)  10 –10 Hadronic contribution from LBL scattering: a  had [ LBL ] = + (12.0 ± 3.5)  10 –10 a  exp – a  SM = (25.2 ± 9.2)  10 –10  2.7 ”standard deviations“ Observed Difference with Experiment: BNL E821 (2004): a  exp =(11 659 208.0  5.8) 10  10 not yet published preliminary SM Theory from ICHEP04 (A. Höcker)

28. B. Lee Roberts, Oxford University, 19 October 2004 - p. 28/55 Hadronic light-by-light This contribution must be determined by calculation. the knowledge of this contribution limits knowledge of theory value.

29. B. Lee Roberts, Oxford University, 19 October 2004 - p. 29/55 a μ is sensitive to a wide range of new physics muon substructure anomalous couplings SUSY (with large tanβ ) many other things (extra dimensions, etc.)

30. B. Lee Roberts, Oxford University, 19 October 2004 - p. 30/55 SUSY connection between a , D μ, μ → e

31. B. Lee Roberts, Oxford University, 19 October 2004 - p. 31/55 Courtesy K.Olive based on Ellis, Olive, Santoso, Spanos In CMSSM, a  can be combined with b → s , cosmological relic density  h 2, and LEP Higgs searches to constrain  mass Allowed  band a  (exp) – a  (e+e- theory) Excluded by direct searches Excluded for neutral dark matter Preferred same discrepancy no discrepancy With expected improvements in a had + E969 the error on the difference

32. B. Lee Roberts, Oxford University, 19 October 2004 - p. 32/55 Spin Precession Frequencies:  in B field The EDM causes the spin to precess out of plane. The motional E - field, β X B, is much stronger than laboratory electric fields. spin difference frequency =  s -  c 0

33. B. Lee Roberts, Oxford University, 19 October 2004 - p. 33/55 Inflector Kicker Modules Storage ring Central orbit Injection orbit Pions Target Protons (from AGS)p=3.1GeV/c Experimental Technique Spin Momentum Muon polarization Muon storage ring injection & kicking focus by Electric Quadrupoles 24 electron calorimeters R=711.2cm d=9cm (1.45T) Electric Quadrupoles polarized 

34. B. Lee Roberts, Oxford University, 19 October 2004 - p. 34/55 muon (g-2) storage ring

35. B. Lee Roberts, Oxford University, 19 October 2004 - p. 35/55 The Storage Ring Magnet r = 7112 mm B 0 = 1.45 T  cyc = 149 ns  (g-2) = 4.37  s   = 64.4  s p  = 3.094 GeV/c

36. B Field Measurement 2001

37. B. Lee Roberts, Oxford University, 19 October 2004 - p. 37/55

38. B. Lee Roberts, Oxford University, 19 October 2004 - p. 38/55 Detectors and vacuum chamber Detector acceptance depends on radial position of the  when it decays.

39. B. Lee Roberts, Oxford University, 19 October 2004 - p. 39/55

40. B. Lee Roberts, Oxford University, 19 October 2004 - p. 40/55 Fourier Transform: residuals to 5-parameter fit beam motion across a scintillating fiber – ~15 turn period

41. B. Lee Roberts, Oxford University, 19 October 2004 - p. 41/55 Where we came from:

42. B. Lee Roberts, Oxford University, 19 October 2004 - p. 42/55 Today with e + e - based theory: All E821 results were obtained with a “blind” analysis.

43. B. Lee Roberts, Oxford University, 19 October 2004 - p. 43/55 Life Beyond E821? With a 2.7  discrepancy, you’ve got to go further. A new upgraded experiment was approved by the BNL PAC in September E969 Goal: total error = 0.2 ppm –lower systematic errors –more beam

44. B. Lee Roberts, Oxford University, 19 October 2004 - p. 44/55 E969: Systematic Error Goal Field improvements will involve better trolley calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware Precession improvements will involve new scraping scheme, lower thresholds, more complete digitization periods, better energy calibration Systematic uncertainty (ppm)1998199920002001E969 Goal Magnetic field –  p 0.50.40.240.170.1 Anomalous precession –  a 0.80.3 0.210.1

45. B. Lee Roberts, Oxford University, 19 October 2004 - p. 45/55 Improved transmission into the ring Inflector Inflector aperture Storage ring aperture E821 Closed EndE821 Prototype Open End

46. B. Lee Roberts, Oxford University, 19 October 2004 - p. 46/55 E969: backward decay beam Pions @ 5.32 GeV/c Decay muons @ 3.094 GeV/c No hadron-induced prompt flash Approximately the same muon flux is realized x 1 more muons Expect for both sides Pedestal vs. Time Near sideFar side E821 E821: Pions @ 3.115 GeV/c  momentum collimator

47. B. Lee Roberts, Oxford University, 19 October 2004 - p. 47/55 Electric and Magnetic Dipole Moments Transformation properties: An EDM implies both P and T are violated. An EDM at a measureable level would imply non-standard model CP. The baryon/antibaryon asymmetry in the universe, needs new sources of CP.

48. B. Lee Roberts, Oxford University, 19 October 2004 - p. 48/55 Present EDM Limits ParticlePresent EDM limit (e-cm) SM value (e-cm) n future exp 10 -24 to 10 -25 *projected

49. B. Lee Roberts, Oxford University, 19 October 2004 - p. 49/55 μ EDM may be enhanced above m μ /m e × e EDM Magnitude increases with magnitude of ν Yukawa couplings and tan β μ EDM greatly enhanced when heavy neutrinos non-degenerate Model Calculations of  EDM

50. B. Lee Roberts, Oxford University, 19 October 2004 - p. 50/55 a μ implications for the muon EDM

51. B. Lee Roberts, Oxford University, 19 October 2004 - p. 51/55 Recall The EDM causes the spin to precess out of plane. EDM Systematic errors are huge in E821 because of (g-2) precession!

52. B. Lee Roberts, Oxford University, 19 October 2004 - p. 52/55 Muon EDM use radial E field to “turn off” g-2 precession so the spin follows the momentum. look for an up-down asymmetry which builds up with time

53. B. Lee Roberts, Oxford University, 19 October 2004 - p. 53/55 Beam Needs: NP 2 the figure of merit is N μ times the polarization. we need to reach the 10 -24 e-cm level. Since SUSY calculations range from 10 -22 to 10 -32 e cm, more muons is better.  = 5*10 -7 (Up-Down)/(Up+Down)

54. B. Lee Roberts, Oxford University, 19 October 2004 - p. 54/55 Summary and Outlook The muon has provided us with much knowledge on how nature works. New experiments on the horizion continue this tradition. Muon (g-2), with a precision of 0.5 ppm, has a 2.7  discrepancy with the standard model. This new physics, if confirmed, would show up in an EDM as well.

55. B. Lee Roberts, Oxford University, 19 October 2004 - p. 55/55 Outlook Scenario 1 –LHC finds SUSY –(g-2), LFV help provide information on important aspects of this new reality; for (g-2) → tan  Scenario 2 –LHC finds the Standard Model Higgs at a reasonable mass, nothing else, (g-2) discrepancy and m might be the only indication of new physics –virtual physics, e.g. (g-2),  EDM,  →e conversion would be even more important. Stay tuned ! Thank you

56. B. Lee Roberts, Oxford University, 19 October 2004 - p. 56/55 Extra slides

57. B. Lee Roberts, Oxford University, 19 October 2004 - p. 57/55 Better agreement between exclusive and inclusive (  2) data than in 1997- 1998 analyses Agreement between Data (BES) and pQCD (within correlated systematic errors) use QCD use data use QCD Evaluating the Dispersion Integral from A. Höcker ICHEP04

58. B. Lee Roberts, Oxford University, 19 October 2004 - p. 58/55 Tests of CVC (A. Höcker – ICHEP04)

59. B. Lee Roberts, Oxford University, 19 October 2004 - p. 59/55 Shape of F  from e + e - and hadronic  decay zoom Comparison between t data and e+e- data from CDM2 (Novosibirsk) New precision data from KLOE confirms CMD2

60. B. Lee Roberts, Oxford University, 19 October 2004 - p. 60/55 The MECO Apparatus Straw Tracker Crystal Calorimeter Muon Stopping Target Muon Beam Stop Superconducting Production Solenoid (5.0 T – 2.5 T) Superconducting Detector Solenoid (2.0 T – 1.0 T) Superconducting Transport Solenoid (2.5 T – 2.1 T) Collimators 10 -17 BR single event sensitivity p beam approved but not funded

61. B. Lee Roberts, Oxford University, 19 October 2004 - p. 61/55 MEG @ PSI (10 -13 BR sensitivity) MEG will start running in 2006

62. B. Lee Roberts, Oxford University, 19 October 2004 - p. 62/55 Experimental bound Largely favoured and confirmed by Kamland Additional contribution to slepton mixing from V 21, matrix element responsible for solar neutrino deficit. (J. Hisano & N. Nomura, Phys. Rev. D59 (1999) 116005). All solar  experiments combined tan(  ) = 30 tan(  ) = 0 MEG goal AfterKamland Connection with oscillations

63. B. Lee Roberts, Oxford University, 19 October 2004 - p. 63/55 E821 ω p systematic errors (ppm) E969 (i ) (I) (II) (III) (iv) *higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time- varying stray fields.

64. B. Lee Roberts, Oxford University, 19 October 2004 - p. 64/55 Systematic errors on ω a (ppm) σ systematic 1999 2000 2001E969 Pile-up0.13 0.080.07 AGS Background0.10 * Lost Muons0.10 0.090.04 Timing Shifts0.100.02 E-Field, Pitch0.080.03*0.05 Fitting/Binning0.070.06* CBO0.050.210.070.04 Beam Debunching0.04 * Gain Change0.020.13 0.03 total0.30.310.210.11 Σ* = 0.11