1. B. Lee Roberts, PSI - 15 August 2006 - p. 1/54 The Muon: A Laboratory for Particle Physics B.L. Roberts Department of Physics Boston University roberts @bu.edu http://physics.bu.edu/roberts.html

2. B. Lee Roberts, PSI - 15 August 2006 - p. 2/54 Outline Introduction to the muon Selected weak interaction parameters Magnetic and electric dipole moments Lepton Flavor Violation Summary and conclusions.

3. B. Lee Roberts, PSI - 15 August 2006 - p. 3/54 The Muon: Discovered in 1936 Discovered in cosmic rays by Seth Neddermeyer and Carl Anderson

4. B. Lee Roberts, PSI - 15 August 2006 - p. 4/54 Confirmed by Street and Stevenson It interacted too weakly with matter to be the “Yukawa” particle which was postulated to carry the nuclear force

5. B. Lee Roberts, PSI - 15 August 2006 - p. 5/54 The discovery of the muon was a big surprise… Lifetime ~2.2  s, practically forever 2 nd generation lepton m   m e = 206.768 277(24) produced polarized –in-flight decay: both “forward” and “backward” muons are highly polarized Paul Scherrer Institut has 10 8  /s in a beam

6. B. Lee Roberts, PSI - 15 August 2006 - p. 6/54 Death of the Muon Decay is self analyzing

7. B. Lee Roberts, PSI - 15 August 2006 - p. 7/54 What have we learn from the  ’s death? The strength of the weak interaction –i.e. the Fermi constant G F (more properly G  ) The fundamental nature of the weak interaction –i.e. is it scalar, vector, tensor, pseudo-scalar, pseudo-vector or pseudo-tensor? Lepton flavor conservation in  -decay VEV of the Higgs field: Induced form-factors in nuclear  -capture

8. B. Lee Roberts, PSI - 15 August 2006 - p. 8/54 from radiative corrections A precise measurement of   + leads to a precise determination of the Fermi constantG F

9. B. Lee Roberts, PSI - 15 August 2006 - p. 9/54 

10. B. Lee Roberts, PSI - 15 August 2006 - p. 10/54   helped predict the mass of the top quark

11. B. Lee Roberts, PSI - 15 August 2006 - p. 11/54   helped predict the mass of the top quark Predictive power in weak sector of SM. Difference between the charged current and neutral current propagators The radiative correction shown above depends on m t 2. Comparisons of charged, vrs. neutral currents gives information on m t.

12. B. Lee Roberts, PSI - 15 August 2006 - p. 12/54 The Electro-Weak Working Group Fits: Predicted Input: G F (17 ppm),  (4 ppb at q 2 =0),  M Z (23 ppm), Measured: from G F The  Lan experiment at PSI will accumulate 10 12  -decays and measure G  to ~1 ppm. If LHC provides a Higgs Mass, then the precision of the confrontation with the SM will greatly improve

13. B. Lee Roberts, PSI - 15 August 2006 - p. 13/54 The Weak Lagrangian (Leptonic Currents) Lepton current is (vector – axial vector) “(V – A)” It might have been: V±A or S±V±A or most general form: Scalar ± Vector ± Weak-Magnitism ± PseudoScalar ± Axial-Vector ± Tensor There have been extensive studies at PSI by Fetscher, Gerber, et al. to look for other couplings in muon decay. Search continues with TWIST at TRIUMF. At present, none have been found.

14. B. Lee Roberts, PSI - 15 August 2006 - p. 14/54 If the Strong Interaction is Present Then we have a more general current, which in principle can have 6 induced form factors in the current.

15. B. Lee Roberts, PSI - 15 August 2006 - p. 15/54 Leptonic and hadronic currents For nuclear   capture (and also in  -decay) there are induced form-factors and the hadronic V-A current contains 6 terms. –in  capture the induced pseudoscaler term becomes important 2 nd class vectorweak magnitismscalar axial vectorpseudoscalar tensor  - decay

16. B. Lee Roberts, PSI - 15 August 2006 - p. 16/54 The Muon Trio: Muon Magnetic Dipole Momoment a  chiral changing Muon EDM

17. B. Lee Roberts, PSI - 15 August 2006 - p. 17/54 The Muon Trio: Muon Magnetic Dipole Momoment a  chiral changing Muon EDM Lepton Flavor Violation

18. B. Lee Roberts, PSI - 15 August 2006 - p. 18/54 (in modern language) (and in English) Magnetic Moments (Field started by Stern)

19. B. Lee Roberts, PSI - 15 August 2006 - p. 19/54 Dirac Equation Predicts g=2 Non-relativistic reduction of the Dirac Equation for an electron in a weak magnetic field.

20. B. Lee Roberts, PSI - 15 August 2006 - p. 20/54 Dirac + Pauli moment Schwinger

21. B. Lee Roberts, PSI - 15 August 2006 - p. 21/54 Radiative corrections change g Dirac Stern-Gerlach Schwinger Kusch-Foley

22. B. Lee Roberts, PSI - 15 August 2006 - p. 22/54 The SM Value for electron and muon anomalies e vrs.  : relative contribution of heavier things e, e*, e, e,e, e,e, e,e, e,e, e,e, e,e, e,e, e,e,

23. B. Lee Roberts, PSI - 15 August 2006 - p. 23/54 a μ is sensitive to a wide range of new physics substructure SUSY (with large tanβ ) many other things (extra dimensions, etc.)

24. B. Lee Roberts, PSI - 15 August 2006 - p. 24/54 We measure the difference frequency between the spin and momentum precession 0 With an electric quadrupole field for vertical focusing

25. B. Lee Roberts, PSI - 15 August 2006 - p. 25/54 Inflector Kicker Modules Storage ring Central orbit Injection orbit Pions Target Protons (from AGS)p=3.1GeV/c Experimental Technique Muon polarization Muon storage ring injection & kicking focus by Electric Quadrupoles 24 electron calorimeters R=711.2cm d=9cm (1.45T) Electric Quadrupoles (from Q. Peng)

26. B. Lee Roberts, PSI - 15 August 2006 - p. 26/54 muon (g-2) storage ring Muon lifetime t  = 64.4  s (g-2) period t a = 4.37  s Cyclotron period t C = 149 ns

27. B. Lee Roberts, PSI - 15 August 2006 - p. 27/54 Detectors and vacuum chamber

28. B. Lee Roberts, PSI - 15 August 2006 - p. 28/54 We count high-energy electrons as a function of time.

29. B. Lee Roberts, PSI - 15 August 2006 - p. 29/54 The ± 1 ppm uniformity in the average field is obtained with special shimming tools. We can shim the dipole, quadrupole sextupole independently 0.5 ppm contours

30. B. Lee Roberts, PSI - 15 August 2006 - p. 30/54 The magnetic field is measured and controlled using pulsed NMR and the free-induction decay. Calibration to a spherical water sample that ties the field to the Larmor frequency of the free proton  p. So we measure  a and  p

31. B. Lee Roberts, PSI - 15 August 2006 - p. 31/54 When we started in 1983, theory and experiment were known to about 10 ppm. Theory uncertainty was ~ 9 ppm Experimental uncertainty was 7.3 ppm

32. B. Lee Roberts, PSI - 15 August 2006 - p. 32/54 E821 achieved 0.5 ppm and the e + e - based theory is also at the 0.6 ppm level. Both can be improved. All E821 results were obtained with a “blind” analysis.

33. B. Lee Roberts, PSI - 15 August 2006 - p. 33/54 To compare with theory, there are two hadronic issues: Lowest order hadronic contribution Hadronic light-by-light ≈

34. B. Lee Roberts, PSI - 15 August 2006 - p. 34/54 Lowest Order Hadronic from e + e - annihilation

35. B. Lee Roberts, PSI - 15 August 2006 - p. 35/54 Two experiments at the Budker Insitute at Novosibirsk have measured R(s) to better than a percent. 1994-1995 114k π+π- 1996 4k π+π- 1997 33k π+π- 1998 ~1M π+π- 2000 ~2M π+π- 96 95,98 97 96,98 98,2000 CMD-2SND  meson interference

36. B. Lee Roberts, PSI - 15 August 2006 - p. 36/54 R(s) measurements at low s VEPP-2M Babar/Belle (ISR) KLOE (ISR) VEPP-2000 At low s the cross-section is measured independently for each final state from Davier/Höcker

37. B. Lee Roberts, PSI - 15 August 2006 - p. 37/54 Taking the hadronic contribution from Simon Eidelman’s talk at ICHEP06, including new CMD2 & SND e + e - data Contributiona , 10 -10 Experiment11 659 208.0 ± 6.3 QED11 658 471.94 ± 0.14 Hadronic 693.1 ± 5.6 Electroweak 15.4 ± 0.1 ± 0.2 Total Theory11 659 180.5 ± 5.6

38. B. Lee Roberts, PSI - 15 August 2006 - p. 38/54 Electric and Magnetic Dipole Moments Phys. Rev. 78 (1950)

39. B. Lee Roberts, PSI - 15 August 2006 - p. 39/54 Transformation Properties of Electric and Magnetic Dipole Moments An EDM implies both P and T are violated. Assuming CPT symmetry, an EDM at a measureable level would imply non-standard model CP.

40. B. Lee Roberts, PSI - 15 August 2006 - p. 40/54 However, it should be emphasized that while such arguments are appealing from the point of view of symmetry, they are not necessarily valid. Ultimately the validity of all such symmetry arguments must rest on experiment. N.F. Ramsey, Phys. Rev. 109, 225 (1958)

41. B. Lee Roberts, PSI - 15 August 2006 - p. 41/54

42. B. Lee Roberts, PSI - 15 August 2006 - p. 42/54 Present EDM Limits ParticlePresent EDM limit (e-cm) SM value (e-cm) n 3 x 10 -26 (90%CL)10 -32 to 10 -31 e-e- 1.6 x 10 -27 (90%CL) < 10 -41  < 10 -38 199 Hg2.1 x 10 -28 (95%CL) *not yet final

43. B. Lee Roberts, PSI - 15 August 2006 - p. 43/54

44. B. Lee Roberts, PSI - 15 August 2006 - p. 44/54 Muon EDM: Naïve scaling would imply that but in some models the dependence is greater.

45. B. Lee Roberts, PSI - 15 August 2006 - p. 45/54 Spin Frequencies:  in B field with MDM & EDM The EDM causes the spin to precess out of plane. The motional E - field, β X B, is much stronger than laboratory electric fields (~GV/m). spin difference frequency =  s -  c 0

46. B. Lee Roberts, PSI - 15 August 2006 - p. 46/54 Dedicated EDM Experiment With  a = 0, the EDM causes the spin to steadily precess out of the plane. 0 Use a radial E-field to turn off the  a precession 

47. B. Lee Roberts, PSI - 15 August 2006 - p. 47/54 “Frozen spin” technique Turn off the (g-2) precession with radial E Look for an up-down asymmetry building up with time

48. B. Lee Roberts, PSI - 15 August 2006 - p. 48/54 A very interesting proposal by Adelmann and Kirch B = 1 T p  = 125 MeV/c   = 0.77,   = 1.57 P ≈ 0.9 E = 0.64 MV/m R = 0.35 m In 1 year of running @ PSI

49. B. Lee Roberts, PSI - 15 August 2006 - p. 49/54 Lepton Flavor Violation (the transition moment) The standard-model gauge bosons do not permit leptons to mix, but new physics at the TeV scale such as SUSY does. Relevant quark level interactions for  -e conversion Dipole Scalar Vector R.Kitano, M.Koike and Y.Okada. 2002

50. B. Lee Roberts, PSI - 15 August 2006 - p. 50/54 SUSY connection between a , D μ, μ → e  → e MDM, EDM ~ ~

51. B. Lee Roberts, PSI - 15 August 2006 - p. 51/54 Past and Future of LFV Limits +e-→-e++e-→-e+ Branching Ratio Limit

52. B. Lee Roberts, PSI - 15 August 2006 - p. 52/54 MEG Experiment (@PSI)   → e   Discovery Potential: Single event sensitivity ~ 1 X 10 -13

53. B. Lee Roberts, PSI - 15 August 2006 - p. 53/54 Summary and Outlook The muon has provided us with much knowledge on how nature works. PSI has played an enormous role in providing this information: e.g. –Search for other couplings in muon decay: (Fetscher, Gerber, et al.,) –Search for LFV: search for    N → e - N search for  + e - →  - e + search for  + → e + e + e - and  + → e +  –Running/Building experiments: muon lifetime - G  muCap - g p MEG - LFV:  + → e + 

54. B. Lee Roberts, PSI - 15 August 2006 - p. 54/54 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 3.3  discrepancy with the standard model. –Upgrade, E969 waits for funding decision in 10/06 This new physics, if confirmed, would show up in an EDM and perhaps LFV as well. MEG is set to turn on and collect data in the next year. Muon-electron conversion holds the best experimental prospect for going much further on LFV. There is plenty of room for new surprises!

55. B. Lee Roberts, PSI - 15 August 2006 - p. 55/54 THE END

56. B. Lee Roberts, PSI - 15 August 2006 - p. 56/54 Extra Slides

57. B. Lee Roberts, PSI - 15 August 2006 - p. 57/54  → e  branching ratio (typical example) SU(5) and SO(10) SUSY GUT SUSY seesaw model The branching ratio can be large in particular for SO(10) SUSY GUT model. J.Hisano and D.Nomura,2000 K.Okumura SO(10) SU(5) Right-handed neutrino mass Right-handed selectron mass MEGA thanks to Y. Okada

58. B. Lee Roberts, PSI - 15 August 2006 - p. 58/54 Comparison of three muon processes in various new physics models SUSY GUT/Seesaw B(  → e  ) >> B(  → 3e) ~ B(  A → eA) Various asymmetries in polarized  decays. SUSY with large tan   → e conv. can be enhanced. Z-dependence in  → e conv. branching ratio. Triplet Higgs for neutrino B(  → 3e) > or ~ B(  → eg) ~B(  A → eA) RL modelB(  → 3e) >> B(  → eg) ~B(  A → eA) Asymmetry in  → 3e RPV SUSYVarious patterns of branching ratios and asymmetries want to measure all three LFV processes to disentangle the models thanks to Y. Okada

59. B. Lee Roberts, PSI - 15 August 2006 - p. 59/54

60. B. Lee Roberts, PSI - 15 August 2006 - p. 60/54  Lan @ PSI aims for a factor of 20 improvement Fit to 2004 data set,  stat ≈ 8.2 ppm

61. B. Lee Roberts, PSI - 15 August 2006 - p. 61/54 Recent Developments: The induced pseudoscalar coupling in nuclear  -capture However, a new TRIUMF measurement of the atomic “ortho to para transition rate” seems to remove much of this problem. Clark, et al., PRL 96, 073401 (2006) further enhanced in radiative muon capture (RMC). TRUIMF experiment saw a 3  discrepancy with PCAC prediction. A new ordinary muon capture (OMC) experiment at PSI, MuCap, hopes to resolve this 3  discrepancy.

62. B. Lee Roberts, PSI - 15 August 2006 - p. 62/54 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 from K. Jungmann

63. B. Lee Roberts, PSI - 15 August 2006 - p. 63/54

64. B. Lee Roberts, PSI - 15 August 2006 - p. 64/54 Pion formfactor (CMD-2) 0.7%0.6% (95)/ 0.8% (98)1.2-4.2% Systematic error published Analysis finished. Not published yet. from: I Logashenko  interference

65. B. Lee Roberts, PSI - 15 August 2006 - p. 65/54

66. B. Lee Roberts, PSI - 15 August 2006 - p. 66/54 a(had) from hadronic  decay? Assume: CVC, no 2 nd -class currents, isospin breaking corrections. –e + e - goes through neutral  –while  -decay goes through charged  n.b.  decay has no isoscalar piece, e + e - does Many inconsistencies in comparison of e + e - and  decay:

67. B. Lee Roberts, PSI - 15 August 2006 - p. 67/54 Testing CVC with one number Infer  branching fractions (more robust than spectral functions) from e + e – data: Difference: BR[  ] – BR[e + e – (CVC) ]: Mode  (  – e + e – ) `S igma‘  –   –  0  + 0.92 ± 0.214.5  –   – 3  0  – 0.08 ± 0.110.7  –  2  –  +  0  + 0.91 ± 0.253.6 ee data on  –  +  0  0 not satisfactory from Michel Davier

68. B. Lee Roberts, PSI - 15 August 2006 - p. 68/54  –   –  0  : preliminary results from BELLE preliminary results from BELLE on   spectral function presented at EPS 2005 high statistics: see dip at 2.4 GeV 2 for first time in  data discrepancies with ALEPH/CLEO at large mass and ee data at low mass

69. B. Lee Roberts, PSI - 15 August 2006 - p. 69/54 The use of  -decay is in question Until the discrepancies between the individual  data sets can be resolved, and CVC can be shown to hold independently it’s clear that only the e + e - data can be used to determine a  (had)  The agreement between SND and CMD-2 invalidates the use of  data until a better understanding of the discrepancies is achieved (an interesting question as such) Michel Davier at Lepton Moments, June 2006

70. B. Lee Roberts, PSI - 15 August 2006 - p. 70/54

71. B. Lee Roberts, PSI - 15 August 2006 - p. 71/54 Model calculations of μ EDM 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 from John Ellis

72. B. Lee Roberts, PSI - 15 August 2006 - p. 72/54 a μ implications for the muon EDM

73. B. Lee Roberts, PSI - 15 August 2006 - p. 73/54 Future Experiments: MECO Experiment @ BNL  - + N → e - + N –10 -17 single event sensitivity proton beam  - /  - collection solenoid  - stopping target straw tracker EM calorimeter Cancelled mu2e @ FNAL???

74. B. Lee Roberts, PSI - 15 August 2006 - p. 74/54 Future Experiments: MECO Experiment @ BNL  - + N → e - + N –10 -17 single event sensitivity MEG Experiment @PSI  + → e +  –Under Construction Data Begins in 2006 Cancelled

75. B. Lee Roberts, PSI - 15 August 2006 - p. 75/54

76. B. Lee Roberts, PSI - 15 August 2006 - p. 76/54 Comparison of three processes If the photon penguin process dominates, there are simple relations among these branching ratios. This is true in many, but not all SUSY modes. thanks to Y. Okada

77. B. Lee Roberts, PSI - 15 August 2006 - p. 77/54 LFV Experiments: MECO Experiment @ BNL  - + N → e - + N –10 -17 single event sensitivity MEG Experiment –Under Construction Data Begins in 2006 PRISM-PRIME  - + N → e - + N –LOI to J-PARC FFAG under construction –10 -18 – 10 -19 single event sensitivity Cancelled