1. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 1/46 Muon Physics at the Front-end of a Neutrino Factory roberts @bu.edu http://g2pc1.bu.edu/~roberts TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA “a particle of uncertain nature” First published muon observation: Paul Kunze, Z. Phys. 83, 1 (1933) Lee Roberts Department of Physics Boston University

2. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 2/46 

3. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 3/46 Outline Introduction to the muon The Muon Trio: –The Magnetic dipole moment: a   –The Electric Dipole Moment d  –Lepton Flavor Violation Other Muon Experiments Summary and conclusions. Some slides/figures have been borrowed from: Klaus Jungmann, Dave Hertzog, Klaus Kirch Jim Miller, Yasuhiro Okada and Andries van der Schaaf

4. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 4/46 Muon properties: Born Polarized Decay is self-analyzing High-energy e ± carry muon spin information!

5. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 5/46 What has the muon done for us (besides being associated with the production of or ) ? The strength of the weak interaction –i.e. the Fermi constant G F (more properly G  ) The V - A nature of the weak interaction Lepton flavor conservation in  -decay (thus far) VEV of the Higgs field: Induced form-factors in nuclear  -capture –complementary to  -decay Constraints on new physics from a , –constrains many models of new physics

6. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 6/46 Theory of Magnetic and Electric Dipole Moments Proc. R. Soc. (London) A117, 610 (1928)

7. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 7/46 Magnetic and Electric Dipole Moments

8. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 8/46 The magnetic dipole moment directed along spin. Dirac + Pauli moment Dirac Theory: g s = 2 For leptons, radiative corrections dominate the value of a ≃ 0.00116… Bottom line: Anomalous moment represents a sum rule over all physics, not just the known physics.

9. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 9/46 Modern Notation: Muon Magnetic Dipole Momoment a  Muon EDM chiral changing

10. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 10/46 The SM Value for the muon anomaly (10 -10 ) # from Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795–881 10 (2) 11 659 178.3 (4.8) Eduardo de Rafael: Theory of the muon anomalous magnetic moment P and T violation at low energies, Heidelberg, Jun - 2008 New BaBar e + e - →  results expected in September

11. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 11/46 a μ is sensitive to a wide range of new physics e.g. SUSY (with large tanβ ) many other things (extra dimensions, etc.)

12. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 12/46  C - cyclotron frequency  S - spin frequency  a - spin turns relative to the momentum Spin Motion in a Magnetic Field 0

13. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 13/46 As spin precesses, the number of high E electrons oscillates with frequency  a. Count number of e - with E thresh ≥ 1.8 GeV Figure of merit: (MDM or EDM)

14. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 14/46 We count high-energy electrons as a function of time.

15. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 15/46 E821 achieved 0.5 ppm and the e + e - based theory is also at the 0.6 ppm level. Difference is 3.4  MdRR=Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795 3.7 

16. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 16/46 The Snowmass Points and Slopes give benchmarks to test observables with model predictions Muon g-2 is a powerful discriminator... no matter where the final value lands! Model Version Expt Future? Present

17. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 17/46 Complementary to LHC data: e.g. a  provides the best measure of  and tan  MSSM reference point SPS1a With these SUSY parameters, LHC gets tan  of 10.22 ± 9.1. See: arXiv:0705.4617v1 [hep-ph]  > 0 by > 6  tan  to < 20% with improvements in theory and experiment things can improve to:

18. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 18/46 The search for a Muon Electric Dipole Moment

19. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 19/46 Purcell and Ramsey: EDM would violate Parity Proposed to search for an EDM of the neutron Phys. Rev. 78 (1950) “raises directly the question of parity.”

20. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 20/46 Electric Dipole Moment: P T If CPT is valid, an EDM would imply non-standard model CP. Transformation Properties

21. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 21/46 The present EDM limits are orders of magnitude from the standard-model value ParticlePresent EDM limit (e-cm) SM value (e-cm) n 199 Hg The discovery of a permanent EDM would change our picture of nature at least as profoundly as the discovery of neutrino mass has!

22. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 22/46 10 -28 Left - Right MSSM  ~  Multi Higgs MSSM  ~ 1 10 -24 10 -22 10 -26 10 -30 10 -32 10 -34 10 -36 e EDM (e.cm) E. Hinds’ e-EDM experiment at Imperial College with YbF molecules is starting to explore this region Standard Model d e < 1.6 x 10 -27 e.cm Commins (2002) Excluded region (Tl atomic beam) with thanks to Ed Hinds n The SUSY CP problem! The strong CP problem! 199 Hg

23. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 23/46 a μ (new physics) implications for d  Either d µ is of order 10 –22 e cm, or the CP phase is strongly suppressed!

24. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 24/46 μ EDM may be enhanced above m μ /m e × e EDM Magnitude increases with magnitude of Yukawa couplings and tan β μ EDM greatly enhanced when heavy neutrinos non-degenerate Model Calculations of  EDM

25. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 25/46 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 (~GV/m). 0

26. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 26/46 Number above (+) and below (-) the midplane will vary as: Total frequency Plane of the spin precession tipped by the angle   aa 

27. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 27/46 E821 looked for this vertical oscillation in 3 ways No significant oscillation was found The observed  a  is not from an EDM at the 2.2  level One can improve significantly at a neutrino factory, since an EDM limit of 10 -23 e ·cm needs NP 2 = 10 16 * Coming soon to a preprint server near you Bottom line: Muon EDM measurement needs the high intensity that could be available at a neutrino factory. Also need modified technique!

28. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 28/46 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  “Frozen spin”

29. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 29/46 “Frozen spin” technique to measure EDM Turn off the (g-2) precession with radial E Up-Down detectors measure EDM asymmetry Look for an up-down asymmetry building up with time Side detectors measure (g-2) precession –To prove the spin is frozen

30. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 30/46 (by A. Streun) PSI suggestion: Adelmann and Kirch hep-ex/0606034 A. Adelmann 1, K. Kirch 1, C.J.G. Onderwater 2, T. Schietinger 1, A. Streun 1 1 PSI, 2 KVI

31. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 31/46 Muon EDM Limits: Present and Future E821 E821: G. Bennett, et al., (Muon g-2 collaboration) to be submitted to PRD 2008 NuFact Need: NA 2 = 10 16 for d  ≃ 10 -23 e ·cm new (g-2) ?

32. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 32/46 SUSY connection between MDM, EDM and the lepton flavor violating transition moment  → e  → e MDM, EDM ~~ SUSY slepton mixing

33. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 33/46 Lepton Flavor Violation 2-body final state  + e - →  - e + Branching Ratio Limit 10 -1 10 -3 10 -5 10 -7 10 -9 10 -11 10 -13 1940 1950 1960 1970 1980 1990 2000 mono-energetic electron

34. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 34/46 Experimental bounds ProcessCurrentFuture 10 -16  2e 10 -16 Comet (Ti) Under some assumptions the  L f = 1 rates are related

35. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 35/46 Presently active:   → e   (MEG @ PSI) First running is going on now –goal < 10 -13

36. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 36/46 Muonic Atom:  - bound in hydrogen-like atomic orbit 1s 2s 2p r Lyman series Balmer series coherent process

37. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 37/46  e - conversion operators have calculated the coherent  - e conversion branching ratios in various nuclei for general LFV interactions to see: (1) which nucleus is the most sensitive to mu-e conversion searches, (2) whether one can distinguish various theoretical models by the Z dependence. Relevant quark level interactions Dipole Scalar Vector R.Kitano, M.Koike and Y.Okada. 2002

38. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 38/46 The branching ratio is largest for the atomic number of Z = 30 – 60. For light nuclei, Z dependences similar for different operators Sizable difference of Z dependences for dipole, scalar and vector interactions (relativistic effect of   ).  -e conversion rate normalized to Al dipolescalarvector providing another way to discriminate different models Kitano, Koike, Okada Bottom line: If you can observe muon- electron conversion, a study of the Z dependence might help sort out which operators contribute.

39. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 39/46 The First  - N  e - N Experiment Steinberger and Wolf After the discovery of the muon it was realized it could decay into an electron and a photon, or convert to an electron in the field of a nucleus. Without lepton flavor conservation, the expected branching fraction for    e +  is about 10 -5 Steinberger and Wolf  - N  e - N, ( 1955 ) R  e < 2  10 -4 Absorbs e - from  - decay Conversion e - reach this counter 9”

40. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 40/46 Two New Proposals for  to e Conversion Experiments  2e at Fermilab –based on MECO / MELC proposals COMET at J-PARC -to be upgraded to PRISM/PRIME SINDRUM II @PSI Data and simulation decay in orbit (simulated) signal prompts suppressed

41. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 41/46 The  2e Apparatus proposed for Fermilab Straw Tracker Crystal Calorimeter Muon Stopping Target 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 p beam Phase 1: 90% C.L. limit of R  e < 6 x 10 -17 Phase 2: 90% C.L. limit of R  e ≲ 10 -18 Proton Target Shielding (Copper) Pions Muons Target Shielding (Tungsten) Protons enter here B=5T B=2.5T

42. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 42/46 COMET Proposal @ J-PARC  e conversion 90% CL R  e < 10 -16 curved detector to reduce low E DIO background

43. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 43/46 R  e < 10 -18 Bottom line: FFAG reduces  p of the muon beam by phase rotation: narrow  t → narrow  p ⇒ thinner stopping target better e - resolution and eliminates the pions which can cause Z N (    background!

44. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 44/46 Flavor oscillations well established in quark sector Predicted M-M Conversion 1957- Named System “Muonium” ? L. Willmann, et al., PRL 82, 49 (1999) Muonium to Anti-muonium Conversion

45. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 45/46 L. Willmann, et al., PRL 82, 49 (1999) (done @PSI) 90% CL:

46. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 46/46 Future Efforts at Existing Facilities (g-2)  –FNAL ? –J-PARC ? MEG –running now!  2e –proposal being prepared for Fermilab COMET/ PRISM/PRIME –proposed to J-PARC, future under discussion Bottom line: The ultimate sensitivity for  e conversion could be reached at the front end of a neutrino factory. The discovery of LFV would also significantly change our view of the world.

47. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 47/46 Summary Muon physics has provided much information in the development of the standard model, including a hint of new physics in a . The electric dipole moment could be measured to a competitive level (to e - ) at a neutrino factory. Muon flavor violation can be pursued to the ultimate sensitivity, or studied systematically at a neutrino factory. The observation of either of these SM “forbidden” effects would be incredibly important in reshaping our view of nature.

48. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 48/46 Extra Projections

49. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 49/46 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.

50. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 50/46 PSI suggestion: 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 A. Adelmann 1, K. Kirch 1, C.J.G. Onderwater 2, T. Schietinger 1, A. Streun 1 hep-ex/0606034

51. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 51/46 Comparison of three muon processes in various new physics models SUSY GUT/Seesaw B(  → e  ) >> B(  → 3e) ~ B(  N → e N ) Various asymmetries in polarized  decays. SUSY with large tan   → e conversion can be enhanced. Z-dependence in  → e conversion BR. Triplet Higgs for neutrino B(  → 3e) > or ~ B(  → e  ) ~B(  N → e N ) RL modelB(  → 3e) >> B(  → eg) ~B(  N → e N ) Asymmetry in  → 3e RPV SUSYVarious patterns of branching ratios and asymmetries want to measure all three LFV processes to disentangle the models

52. B. Lee Roberts, NuFact2008 4 July 2008 - p. 52/46  e Conversion is sensitive to a wide range of new physics Compositeness Second Higgs doublet Heavy Z’, Anomalous Z coupling Predictions at 10 -15 Supersymmetry Heavy Neutrinos Leptoquarks After W. Marciano

53. B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 53/46   → 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 MEG tan  = 3 tan  = 10 tan  = 30