B. Lee Roberts, PSI - 15 August p. 1/54 The Muon: A Laboratory for Particle Physics B.L. Roberts Department of Physics Boston University

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

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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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 = (24) produced polarized –in-flight decay: both “forward” and “backward” muons are highly polarized Paul Scherrer Institut has 10 8  /s in a beam

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

B. Lee Roberts, PSI - 15 August 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

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

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

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

B. Lee Roberts, PSI - 15 August 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.

B. Lee Roberts, PSI - 15 August 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  -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

B. Lee Roberts, PSI - 15 August 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.

B. Lee Roberts, PSI - 15 August 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.

B. Lee Roberts, PSI - 15 August 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

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

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

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

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

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

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

B. Lee Roberts, PSI - 15 August 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,

B. Lee Roberts, PSI - 15 August 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.)

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

B. Lee Roberts, PSI - 15 August 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)

B. Lee Roberts, PSI - 15 August 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

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

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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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.

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

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

B. Lee Roberts, PSI - 15 August p. 35/54 Two experiments at the Budker Insitute at Novosibirsk have measured R(s) to better than a percent k π+π k π+π k π+π ~1M π+π ~2M π+π , ,98 98,2000 CMD-2SND  meson interference

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August p. 37/54 Taking the hadronic contribution from Simon Eidelman’s talk at ICHEP06, including new CMD2 & SND e + e - data Contributiona , Experiment ± 6.3 QED ± 0.14 Hadronic ± 5.6 Electroweak 15.4 ± 0.1 ± 0.2 Total Theory ± 5.6

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

B. Lee Roberts, PSI - 15 August 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.

B. Lee Roberts, PSI - 15 August 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)

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

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

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

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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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 

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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 PSI

B. Lee Roberts, PSI - 15 August 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

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

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

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

B. Lee Roberts, PSI - 15 August 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 + 

B. Lee Roberts, PSI - 15 August 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!

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

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

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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

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

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

B. Lee Roberts, PSI - 15 August 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, (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.

B. Lee Roberts, PSI - 15 August p. 62/54 Muonium Hydrogen (without the proton) Zeeman splitting    p = (37) (120 ppb) where  p comes from proton NMR in the same B field from K. Jungmann

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

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

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

B. Lee Roberts, PSI - 15 August 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:

B. Lee Roberts, PSI - 15 August 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  ±  –   – 3  0  – 0.08 ±  –  2  –  +  0  ± ee data on  –  +  0  0 not satisfactory from Michel Davier

B. Lee Roberts, PSI - 15 August 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

B. Lee Roberts, PSI - 15 August 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

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

B. Lee Roberts, PSI - 15 August 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

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

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

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

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

B. Lee Roberts, PSI - 15 August 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

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