B. Lee Roberts, NuFact2008 – 4 July p. 1/46 Muon Physics at the Front-end of a Neutrino Factory 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

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

B. Lee Roberts, NuFact2008 – 4 July 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

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

B. Lee Roberts, NuFact2008 – 4 July 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

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

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

B. Lee Roberts, NuFact2008 – 4 July 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 ≃ … Bottom line: Anomalous moment represents a sum rule over all physics, not just the known physics.

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

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

B. Lee Roberts, NuFact2008 – 4 July 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.)

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

B. Lee Roberts, NuFact2008 – 4 July 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)

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

B. Lee Roberts, NuFact2008 – 4 July 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) 

B. Lee Roberts, NuFact2008 – 4 July 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

B. Lee Roberts, NuFact2008 – 4 July 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 ± 9.1. See: arXiv: v1 [hep-ph]  > 0 by > 6  tan  to < 20% with improvements in theory and experiment things can improve to:

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

B. Lee Roberts, NuFact2008 – 4 July 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.”

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

B. Lee Roberts, NuFact2008 – 4 July 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!

B. Lee Roberts, NuFact2008 – 4 July p. 22/ Left - Right MSSM  ~  Multi Higgs MSSM  ~ 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 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

B. Lee Roberts, NuFact2008 – 4 July 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!

B. Lee Roberts, NuFact2008 – 4 July 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

B. Lee Roberts, NuFact2008 – 4 July 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

B. Lee Roberts, NuFact2008 – 4 July 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 

B. Lee Roberts, NuFact2008 – 4 July 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 e ·cm needs NP 2 = * 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!

B. Lee Roberts, NuFact2008 – 4 July 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”

B. Lee Roberts, NuFact2008 – 4 July 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

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

B. Lee Roberts, NuFact2008 – 4 July 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 = for d  ≃ e ·cm new (g-2) ?

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

B. Lee Roberts, NuFact2008 – 4 July p. 33/46 Lepton Flavor Violation 2-body final state  + e - →  - e + Branching Ratio Limit mono-energetic electron

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

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

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

B. Lee Roberts, NuFact2008 – 4 July 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

B. Lee Roberts, NuFact2008 – 4 July 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.

B. Lee Roberts, NuFact2008 – 4 July 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 Steinberger and Wolf  - N  e - N, ( 1955 ) R  e < 2  Absorbs e - from  - decay Conversion e - reach this counter 9”

B. Lee Roberts, NuFact2008 – 4 July 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 Data and simulation decay in orbit (simulated) signal prompts suppressed

B. Lee Roberts, NuFact2008 – 4 July 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 Phase 2: 90% C.L. limit of R  e ≲ Proton Target Shielding (Copper) Pions Muons Target Shielding (Tungsten) Protons enter here B=5T B=2.5T

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

B. Lee Roberts, NuFact2008 – 4 July p. 43/46 R  e < 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!

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

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

B. Lee Roberts, NuFact2008 – 4 July 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.

B. Lee Roberts, NuFact2008 – 4 July 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.

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

B. Lee Roberts, NuFact2008 – 4 July 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.

B. Lee Roberts, NuFact2008 – 4 July 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 PSI A. Adelmann 1, K. Kirch 1, C.J.G. Onderwater 2, T. Schietinger 1, A. Streun 1 hep-ex/

B. Lee Roberts, NuFact2008 – 4 July 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

B. Lee Roberts, NuFact July 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 Supersymmetry Heavy Neutrinos Leptoquarks After W. Marciano

B. Lee Roberts, NuFact2008 – 4 July 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