B. Lee Roberts, Oxford University, 19 October p. 1/55 The Muon: A Laboratory for Particle Physics Everything you always wanted to know about the muon but were afraid to ask. B. Lee Roberts Department of Physics Boston University

B. Lee Roberts, Oxford University, 19 October p. 2/55 Outline Introduction to the muon Selected weak interaction parameters Muonium Lepton Flavor Violation Magnetic and electric dipole moments Summary and conclusions.

B. Lee Roberts, Oxford University, 19 October p. 3/55 The Muon (“Who ordered that?”) Lifetime ~2.2  s, practically forever 2 nd generation lepton m   m e = (24) produced polarized For decay in flight, “forward” and “backward” muons are highly polarized.

B. Lee Roberts, Oxford University, 19 October p. 4/55 The Muon – ctd. Decay is self analyzing It can be produced copiously in pion decay –PSI has 10 8  /s in a new beam

B. Lee Roberts, Oxford University, 19 October p. 5/55 A precise measurement of   + leads to a precise determination of G F Predictive power in weak sector of SM: Top quark mass prediction:m t = 177  20 GeV Input: G F (17 ppm),  (4 ppb at q 2 =0), M Z (23 ppm), 2004 Update from D0m t = 178  4.3 GeV

B. Lee Roberts, Oxford University, 19 October p. 6/55  PSI aims for a factor of 20 improvement

B. Lee Roberts, Oxford University, 19 October p. 7/55 The Leptonic Currents Lepton current is (V – A) There have been extensive studies at PSI by Gerber, Fetscher, et al. to look for other couplings in muon decay.

B. Lee Roberts, Oxford University, 19 October p. 8/55 Leptonic and hadronic currents For nuclear   capture there are induced formfactors and the hadronic current contains 6 terms. –the induced pseudoscaler term is important further enhanced in radiative muon capture A new experiment at PSI MuCap hopes to resolve the present 3  discrepancy with PCAC

B. Lee Roberts, Oxford University, 19 October p. 9/55 Muonium Hydrogen (without the proton) Zeeman splitting    p = (37) (120 ppb) where  p comes from proton NMR in the same B field

B. Lee Roberts, Oxford University, 19 October p. 10/55 muonium and hydrogen hfs → proton structure

B. Lee Roberts, Oxford University, 19 October p. 11/55 Lepton Flavor We have found empirically that lepton number is conserved in muon decay and in beta decay. –e.g. What about or

B. Lee Roberts, Oxford University, 19 October p. 12/55 General Statements We know that oscillate –neutral lepton flavor violation Expect charged lepton flavor violation at some level –enhanced if there is new dynamics at the TeV scale in particular if there is SUSY We expect CP in the lepton sector (EDMs as well as oscillations) –possible connection with cosmology (leptogenesis)

B. Lee Roberts, Oxford University, 19 October p. 13/55 The Muon Trio: Lepton Flavor Violation Muon MDM (g-2) chiral changing Muon EDM

B. Lee Roberts, Oxford University, 19 October p. 14/55 Past and Future of LFV Limits +e-→-e++e-→-e+ MEG  → e  – BR sensitivity under construction at PSI, first data in 2006 MECO  + +A→e + +A – BR sensitivity approved at Brookhaven, not yet funded (Needs Congressional approval) Branching Ratio Limit

B. Lee Roberts, Oxford University, 19 October p. 15/55 Magnetic Dipole Moments The field was started by Stern

B. Lee Roberts, Oxford University, 19 October p. 16/55 Z. Phys. 7, 249 (1921)

B. Lee Roberts, Oxford University, 19 October p. 17/55 (in modern language) 673 (1924)

B. Lee Roberts, Oxford University, 19 October p. 18/55 Dirac + Pauli moment

B. Lee Roberts, Oxford University, 19 October p. 19/55 Dirac Equation Predicts g=2 radiative corrections change g

B. Lee Roberts, Oxford University, 19 October p. 20/55 The CERN Muon (g-2) Experiments The muon was shown to be a point particle obeying QED The final CERN precision was 7.3 ppm

B. Lee Roberts, Oxford University, 19 October p. 21/55 Standard Model Value for (g-2) relative contribution of heavier things

B. Lee Roberts, Oxford University, 19 October p. 22/55 Two Hadronic Issues: Lowest order hadronic contribution Hadronic light-by-light

B. Lee Roberts, Oxford University, 19 October p. 23/55 Lowest Order Hadronic from e + e - annihilation

B. Lee Roberts, Oxford University, 19 October p. 24/55 a(had) from hadronic  decay? Assume: CVC, no 2 nd -class currents, isospin breaking corrections. n.b.  decay has no isoscalar piece, while e + e - does Many inconsistencies in comparison of e + e - and  decay: - Using CVC to predict  branching ratios gives 0.7 to 3.6  discrepancies with reality. - F  from  decay has different shape from e + e -.

B. Lee Roberts, Oxford University, 19 October p. 25/55 Comparison with CMD-2 in the Energy Range 0.37 < s p <0.93 GeV 2 (375.6  0.8 stat  4.9 syst+theo ) (378.6  2.7 stat  2.3 syst+theo ) KLOE CMD2 1.3 % Error 0.9 % Error a   = (  0.8 stat  3.5 syst  3.5 theo ) p contribution to a m hadr KLOE has evaluated the Dispersions Integral for the 2-Pion-Channel in the Energy Range 0.35 < s p <0.95 GeV 2 At large values of s  (>m   ) KLOE is consistent with CMD and therefore They confirm the deviation from t -data!. Pion Formfactor CMD-2 KLOE s  [GeV 2 ] KLOE Data on R(s) Courtesy of G. Venanzone

B. Lee Roberts, Oxford University, 19 October p. 26/55 A. Höcker at ICHEP04

B. Lee Roberts, Oxford University, 19 October p. 27/55 a  had [e + e – ] = (693.4 ± 5.3 ± 3.5)  10 –10 a  SM [e + e – ] = ( ± 6.3 had ± 3.5 LBL ± 0.3 QED+EW )  10 –10 Weak contribution a  weak = + (15.4 ± 0.3)  10 –10 Hadronic contribution from higher order : a  had [(  /  ) 3 ] = – (10.0 ± 0.6)  10 –10 Hadronic contribution from LBL scattering: a  had [ LBL ] = + (12.0 ± 3.5)  10 –10 a  exp – a  SM = (25.2 ± 9.2)  10 –10  2.7 ”standard deviations“ Observed Difference with Experiment: BNL E821 (2004): a  exp =(  5.8) 10  10 not yet published preliminary SM Theory from ICHEP04 (A. Höcker)

B. Lee Roberts, Oxford University, 19 October p. 28/55 Hadronic light-by-light This contribution must be determined by calculation. the knowledge of this contribution limits knowledge of theory value.

B. Lee Roberts, Oxford University, 19 October p. 29/55 a μ is sensitive to a wide range of new physics muon substructure anomalous couplings SUSY (with large tanβ ) many other things (extra dimensions, etc.)

B. Lee Roberts, Oxford University, 19 October p. 30/55 SUSY connection between a , D μ, μ → e

B. Lee Roberts, Oxford University, 19 October p. 31/55 Courtesy K.Olive based on Ellis, Olive, Santoso, Spanos In CMSSM, a  can be combined with b → s , cosmological relic density  h 2, and LEP Higgs searches to constrain  mass Allowed  band a  (exp) – a  (e+e- theory) Excluded by direct searches Excluded for neutral dark matter Preferred same discrepancy no discrepancy With expected improvements in a had + E969 the error on the difference

B. Lee Roberts, Oxford University, 19 October p. 32/55 Spin Precession Frequencies:  in B field 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, Oxford University, 19 October p. 33/55 Inflector Kicker Modules Storage ring Central orbit Injection orbit Pions Target Protons (from AGS)p=3.1GeV/c Experimental Technique Spin Momentum Muon polarization Muon storage ring injection & kicking focus by Electric Quadrupoles 24 electron calorimeters R=711.2cm d=9cm (1.45T) Electric Quadrupoles polarized 

B. Lee Roberts, Oxford University, 19 October p. 34/55 muon (g-2) storage ring

B. Lee Roberts, Oxford University, 19 October p. 35/55 The Storage Ring Magnet r = 7112 mm B 0 = 1.45 T  cyc = 149 ns  (g-2) = 4.37  s   = 64.4  s p  = GeV/c

B Field Measurement 2001

B. Lee Roberts, Oxford University, 19 October p. 37/55

B. Lee Roberts, Oxford University, 19 October p. 38/55 Detectors and vacuum chamber Detector acceptance depends on radial position of the  when it decays.

B. Lee Roberts, Oxford University, 19 October p. 39/55

B. Lee Roberts, Oxford University, 19 October p. 40/55 Fourier Transform: residuals to 5-parameter fit beam motion across a scintillating fiber – ~15 turn period

B. Lee Roberts, Oxford University, 19 October p. 41/55 Where we came from:

B. Lee Roberts, Oxford University, 19 October p. 42/55 Today with e + e - based theory: All E821 results were obtained with a “blind” analysis.

B. Lee Roberts, Oxford University, 19 October p. 43/55 Life Beyond E821? With a 2.7  discrepancy, you’ve got to go further. A new upgraded experiment was approved by the BNL PAC in September E969 Goal: total error = 0.2 ppm –lower systematic errors –more beam

B. Lee Roberts, Oxford University, 19 October p. 44/55 E969: Systematic Error Goal Field improvements will involve 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

B. Lee Roberts, Oxford University, 19 October p. 45/55 Improved transmission into the ring Inflector Inflector aperture Storage ring aperture E821 Closed EndE821 Prototype Open End

B. Lee Roberts, Oxford University, 19 October p. 46/55 E969: backward decay beam 5.32 GeV/c Decay GeV/c No hadron-induced prompt flash Approximately the same muon flux is realized x 1 more muons Expect for both sides Pedestal vs. Time Near sideFar side E821 E821: GeV/c  momentum collimator

B. Lee Roberts, Oxford University, 19 October p. 47/55 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, Oxford University, 19 October p. 48/55 Present EDM Limits ParticlePresent EDM limit (e-cm) SM value (e-cm) n future exp to *projected

B. Lee Roberts, Oxford University, 19 October p. 49/55 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, Oxford University, 19 October p. 50/55 a μ implications for the muon EDM

B. Lee Roberts, Oxford University, 19 October p. 51/55 Recall The EDM causes the spin to precess out of plane. EDM Systematic errors are huge in E821 because of (g-2) precession!

B. Lee Roberts, Oxford University, 19 October p. 52/55 Muon EDM use radial E field to “turn off” g-2 precession so the spin follows the momentum. look for an up-down asymmetry which builds up with time

B. Lee Roberts, Oxford University, 19 October p. 53/55 Beam Needs: NP 2 the figure of merit is N μ times the polarization. we need to reach the e-cm level. Since SUSY calculations range from to e cm, more muons is better.  = 5*10 -7 (Up-Down)/(Up+Down)

B. Lee Roberts, Oxford University, 19 October p. 54/55 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 2.7  discrepancy with the standard model. This new physics, if confirmed, would show up in an EDM as well.

B. Lee Roberts, Oxford University, 19 October p. 55/55 Outlook Scenario 1 –LHC finds SUSY –(g-2), LFV help provide information on important aspects of this new reality; for (g-2) → tan  Scenario 2 –LHC finds the Standard Model Higgs at a reasonable mass, nothing else, (g-2) discrepancy and m might be the only indication of new physics –virtual physics, e.g. (g-2),  EDM,  →e conversion would be even more important. Stay tuned ! Thank you

B. Lee Roberts, Oxford University, 19 October p. 56/55 Extra slides

B. Lee Roberts, Oxford University, 19 October p. 57/55 Better agreement between exclusive and inclusive (  2) data than in analyses Agreement between Data (BES) and pQCD (within correlated systematic errors) use QCD use data use QCD Evaluating the Dispersion Integral from A. Höcker ICHEP04

B. Lee Roberts, Oxford University, 19 October p. 58/55 Tests of CVC (A. Höcker – ICHEP04)

B. Lee Roberts, Oxford University, 19 October p. 59/55 Shape of F  from e + e - and hadronic  decay zoom Comparison between t data and e+e- data from CDM2 (Novosibirsk) New precision data from KLOE confirms CMD2

B. Lee Roberts, Oxford University, 19 October p. 60/55 The MECO Apparatus Straw Tracker Crystal Calorimeter Muon Stopping Target Muon Beam Stop 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 BR single event sensitivity p beam approved but not funded

B. Lee Roberts, Oxford University, 19 October p. 61/55 PSI ( BR sensitivity) MEG will start running in 2006

B. Lee Roberts, Oxford University, 19 October p. 62/55 Experimental bound Largely favoured and confirmed by Kamland Additional contribution to slepton mixing from V 21, matrix element responsible for solar neutrino deficit. (J. Hisano & N. Nomura, Phys. Rev. D59 (1999) ). All solar  experiments combined tan(  ) = 30 tan(  ) = 0 MEG goal AfterKamland Connection with oscillations

B. Lee Roberts, Oxford University, 19 October p. 63/55 E821 ω p systematic errors (ppm) E969 (i ) (I) (II) (III) (iv) *higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time- varying stray fields.

B. Lee Roberts, Oxford University, 19 October p. 64/55 Systematic errors on ω a (ppm) σ systematic E969 Pile-up AGS Background0.10 * Lost Muons Timing Shifts E-Field, Pitch *0.05 Fitting/Binning * CBO Beam Debunching0.04 * Gain Change total Σ* = 0.11