B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 1/39 Muon Physics at the Front End of a  Factory An introduction B. Lee Roberts Boston University with some theory projections taken from Yasuhiro Okada KEK bu.edu

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 2/39 Outline Introduction to the muon G F Lepton Flavor Violation Magnetic and electric dipole moments Summary and conclusions.

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 3/39 The Muon (“Who ordered that?”) Lifetime ~2.2  s, practically forever 2 nd generation lepton m   m e = (24) produced polarized –in-flight decay: both “forward” and “backward” muons qre highly polarized Paul Scherrer Institut has 10 8  /s in a beam

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 4/39 What can we learn from the  ’s death? The strength of the weak interaction –i.e. the Fermi constant G F The fundamental nature of the low-energy weak interaction –i.e. is it scalar, vector, tensor, pseudo-scalar, pseudo-vector or pseudo-tensor?

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 5/39   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 ISS Plenary Meeting: RAL 26 April p. 6/39 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 GF to ~1 ppm. If LHC provides a Higgs Mass, then the precision of the confrontation with the SM will greatly improve

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 7/39 The Muon Trio: LFV, MDM, EDM Lepton Flavor Violation The standard-model gauge bosons do not permit leptons to mix, but new physics at the TeV scale such as SUSY does.

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 8/39 SUSY GUT and SUSY Seesaw model The flavor off-diagonal terms in the slepton mass matrix are induced by renormalization effects due to GUT and/or neutrino interactions. M planck GUT Yukawa interaction Neutrino Yukawa interaction CKM matrixNeutrino oscillation L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 9/39 Many models beyond the S-M contain sources of LFV Although the simple seesaw or Dirac neutrino model predicts too small generate branching ratios for the charged lepton LFV, other models of neutrino mass generation can induce observable effects. For example: – Generalized Zee model (K.Hasagawa, C.S.Lim, K.Ogure, 2003) – Neutrino mass from the warped extra dimension (R.Kitano,2000) – R-parity violating SUSY model (A.de Gouvea,S.Lola,K.Tobe,2001) –Triplet Higgs model (E.J.Chun, K.Y.Lee,S.C.Park; N.Kakizaki,Y.Ogura, F.Shima, 2003) –Left-right symmetric model (V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004) –SUSY seesaw model (F.Borzumati and A.Masiero 1986)

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 10/39 Experimental bounds ProcessCurrentFuture (Ti)  → e conversion search at the level of is proposed in the future muon facility at J-PARC (PRIME).

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 11/39 Past and Future of LFV Limits +e-→-e++e-→-e+ Branching Ratio Limit

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 12/39  → 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

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 13/39 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 ISS Plenary Meeting: RAL 26 April p. 14/39 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 model B(  →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

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 15/39 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 any flavor conservation, the expected branching fraction for  +  e+  is about Steinberger and Wolf first looked for  - N  e - N, publishing a null result in 1955, R  e < 2  Absorbs e - from  - decay Conversion e - reach this counter 9”

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 16/39 Z dependence of mu-e conversion branching ratio have calculated the coherent mu-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 ISS Plenary Meeting: RAL 26 April p. 17/39 The branching ratio is largest for the atomic number of Z=30 – 60. For light nuclei, Z dependences are similar for different operator forms. Sizable difference of Z dependences for dipole, scalar and vector interactions. This is due to a relativistic effect of the muon wave function.  -e conversion rate normalized to Al dipole scalar vector providing another way to discriminate different models Kitano, Koike, Okada

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 18/39 The Muon Trio: MDM, EDM Muon MDM (g-2) chiral changing Muon EDM

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 19/39 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.

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 20/39 SUSY connection between a , D μ, μ → e  → e MDM, EDM ~ ~

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 21/39 Magnetic Dipole moments Field invented by Otto Stern in 1921

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 22/39 (in modern language)

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 23/39 Dirac + Pauli moment

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 24/39 Non-Standard Model Value for Muon (g-2) ? e vrs.  : relative contribution of heavier things ? S

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 25/39 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 ISS Plenary Meeting: RAL 26 April p. 26/39 The hadronic contribution to a   has to come from data

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 27/39 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. world average

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 28/39 Based on the latest report on e + e - → hadrons there is an apparent discrepancy at the level of 2.9 ... A new experiment at BNL (E969) could improve the confrontation with theory by a factor of 2 What implications might the possible (g-2) discrepancy have for muon physics at a neutrino factory? –New physics at the TeV scale? Could one do 10 times better? A few words about the technique which is important to understand for the EDM experiment

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 29/39 We measure the difference frequency between the spin and momentum precession 0 With an electric quadrupole field for vertical focusing

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 30/39 The 700 ton (g-2)  precision storage ring Muon lifetime t  = 64.4  s (g-2) period t a = 4.37  s Cyclotron period t C = 149 ns Scraping time (E821) 7 to 15  s Total counting time ~700  s Total number of turns ~4000

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 31/39 The magnetic field is measured and controlled using pulsed NMR, and the muon spin precession is measured using  →e  decay

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 32/39 (g-2) ten times better (0.05 ppm) ? Need to know to 0.01 ppm (10 ppb) Need ~10 14 polarized muons at ≥ 3 GeV/c momentum Need substantial improvements in theory for the result to be interpreted

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 33/39 Present EDM Limits ParticlePresent EDM limit (e-cm) SM value (e-cm) n future  exp to *projected

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 34/39 Naïve scaling would imply that but in some models the dependence is greater, e.g.

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 35/39 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

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 36/39 a μ implications for the muon EDM

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 37/39 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. spin difference frequency =  s -  c 0

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 38/39 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 ISS Plenary Meeting: RAL 26 April p. 39/39 In the next talk, Klaus Jungmann will give a few more details on a dedicated muon EDM experiment.

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 40/39 Summary and Conclusions There are a number of interesting topics which can be pursued at a high intensity muon source –Lepton Flavor Violation –Search for a permanent EDM of the muon are the most compelling The next talk will cover these topics in more detail

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 41/39 Extra Projections

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 42/39 The error budget for E969 represents a continuation of improvements already made during E821 Field improvements: 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) E969 Goal Magnetic field –  p Anomalous precession –  a Statistical uncertainty (ppm) Total Uncertainty (ppm)

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 43/39

B. Lee Roberts ISS Plenary Meeting: RAL 26 April p. 44/39