B. Lee Roberts, College of William and Mary, 24 March p. 1/61 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, College of William and Mary, 24 March p. 2/61 Outline Introduction to the muon Selected weak interaction parameters Muonium Lepton Flavor Violation Magnetic and electric dipole moments Summary and conclusions.

B. Lee Roberts, College of William and Mary, 24 March p. 3/61 The Muon: Discovered in 1936 Discovered in cosmic rays by Seth Neddermeyer and Carl Anderson

B. Lee Roberts, College of William and Mary, 24 March p. 4/61 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, College of William and Mary, 24 March p. 5/61 The Muon’s Discovery was a big surprise Lifetime ~2.2  s, practically forever 2 nd generation lepton m   m e = (24) I. I. Rabi

B. Lee Roberts, College of William and Mary, 24 March p. 6/61 The Standard Model (Our Periodic Table) Interact weakly through the Leptons e  e   Interact strongly through the gluons g Electroweak gage bosons  Z0Z0 W±W± Quarks ust dcb

B. Lee Roberts, College of William and Mary, 24 March p. 7/61 Production of The Muon produced polarized from the death of a pion For  decay in flight, “forward” and “backward” muons are highly polarized. It can be produced copiously in pion decay e.g. Paul Scherrer Institut has 10 8  /s in a beam

B. Lee Roberts, College of William and Mary, 24 March p. 8/61 Death of the Muon Decay is self analyzing

B. Lee Roberts, College of William and Mary, 24 March p. 9/61 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 weak interaction –i.e. is it scalar, vector, tensor, pseudo-scalar, pseudo-vector or pseudo- tensor?

B. Lee Roberts, College of William and Mary, 24 March p. 10/61 from radiative corrections A precise measurement of   + leads to a precise determination of the Fermi constantG F

B. Lee Roberts, College of William and Mary, 24 March p. 11/61 

B. Lee Roberts, College of William and Mary, 24 March p. 12/61   helped predict the mass of the top quark Predictive power in weak sector of SM. Difference between the charged and neutral current propagator: 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, College of William and Mary, 24 March p. 13/61 Experiment at a glance 1.Collect handful of muons in a few  s 2.Turn off beam 3.Watch them decay 4.Repeat e+e+ Time  in target Accum. Period Measurement Period

B. Lee Roberts, College of William and Mary, 24 March p. 14/61  Paul Scherrer Institut aims for a factor of 20 improvement on  

B. Lee Roberts, College of William and Mary, 24 March p. 15/61 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 Gerber, Fetscher, et al. to look for other couplings in muon decay. None were found

B. Lee Roberts, College of William and Mary, 24 March p. 16/61 If the Strong Interaction is Present Then we have a more general current, which in principle can have all 6 of these components to the current.

B. Lee Roberts, College of William and Mary, 24 March p. 17/61 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. –the induced pseudoscaler term is important 2 nd class vectorweak magnitismscalar axial vectorpseudoscalar tensor

B. Lee Roberts, College of William and Mary, 24 March p. 18/61 An Aside: but stop the press! new measurement of the atomic “ortho to para transition rate” seems to remove much of this problem, Clark, Armstrong, et al., PRL 96, (2006) The induced pseudoscalar coupling in  - capture further enhanced in radiative muon capture A new experiment at PSI MuCap hopes to resolve the present 3  discrepancy with PCAC

B. Lee Roberts, College of William and Mary, 24 March p. 19/61 Muonium  + e - (not  +  - ) Hydrogen (without the proton) Named by Val Telegdi discovered by Vernon Hughes

B. Lee Roberts, College of William and Mary, 24 March p. 20/61 Muonium Zeeman splitting    p = (37) (120 ppb) where  p comes from proton NMR in the same B field

B. Lee Roberts, College of William and Mary, 24 March p. 21/61 muonium and hydrogen hfs → proton structure

B. Lee Roberts, College of William and Mary, 24 March p. 22/61 Lepton Flavor Remember the puzzle with  -decay? –it appeared that energy conservation did not hold in the decay n → p + e - which should have a mono-energetic e + in the final state. e-e-

B. Lee Roberts, College of William and Mary, 24 March p. 23/61 Lepton Flavor It took Pauli to propose that energy was conserved, but there was a new neutral particle emitted in the decay (named neutrino by Fermi), so the decay was a 3-body decay with a continuous spectrum.

B. Lee Roberts, College of William and Mary, 24 March p. 24/61 Lepton Flavor We have found empirically that lepton family number is conserved in muon decay. –e.g. What about or

B. Lee Roberts, College of William and Mary, 24 March p. 25/61 Lepton Flavor in Muon Decay m e = MeV m m = MeV Why don’t we see   → e +  ? Neutrinos oscillate – however, the predicted Standard Model Charged Lepton Flavor Violation unmeasureably small (from loops). The standard model gauge bosons (interactions) do not permit lepton flavor-changing interactions, i.e. there is conservation of each lepton flavor separately.

B. Lee Roberts, College of William and Mary, 24 March p. 26/61 SM charged leptons do not mix Expect charged lepton flavor to be enhanced if there is new dynamics at the TeV scale, in particular if there is Supersymmetry

B. Lee Roberts, College of William and Mary, 24 March p. 27/61 In Standard Model we have: antiparticles particles supersymmetric partners (spartners) SUSY: (with thanks to Bruce Winstein)

B. Lee Roberts, College of William and Mary, 24 March p. 28/61 Supersymmetry Permits Charged Lepton Mixing In supersymmetry there is mixing between the charged sleptons Many people believe that SUSY is the new physics which will be found at LHC

B. Lee Roberts, College of William and Mary, 24 March p. 29/61 Beyond the SM: The Muon Trio: Lepton Flavor Violation Muon MDM (g-2) chiral changing Muon EDM

B. Lee Roberts, College of William and Mary, 24 March p. 30/61 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 looked for  - N  e - N for the first time, publishing a null result in 1955, with a limit R  e < 2  Absorbs e - from  - decay Conversion e - reach this counter 9”

B. Lee Roberts, College of William and Mary, 24 March p. 31/61 The MECO Experiment Muon Beam Stop Superconducting Production Solenoid (5.0 T – 2.5 T) Superconducting Transport Solenoid (2.5 T – 2.1 T) Straw Tracker Crystal Calorimeter Muon Stopping Target Superconducting Detector Solenoid (2.0 T – 1.0 T) Collimators BR single event sensitivity p beam

B. Lee Roberts, College of William and Mary, 24 March p. 32/61 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 Was approved at Brookhaven, not funded Branching Ratio Limit

B. Lee Roberts, College of William and Mary, 24 March p. 33/61 Electric and Magnetic Dipole Moments In 1950, Purcell and Ramsey propose to search for a neutron EDM to check parity violation In 1957, Landau and Ramsey independently point out that an EDM violates both P and T

B. Lee Roberts, College of William and Mary, 24 March p. 34/61 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, College of William and Mary, 24 March p. 35/61 Present EDM Limits ParticlePresent EDM limit (e-cm) SM value (e-cm) n future exp to *projected

B. Lee Roberts, College of William and Mary, 24 March p. 36/61 Magnetic Dipole Moments The field was started by Otto Stern

B. Lee Roberts, College of William and Mary, 24 March p. 37/61 Z. Phys. 7, 249 (1921)

B. Lee Roberts, College of William and Mary, 24 March p. 38/61 (in modern language)

B. Lee Roberts, College of William and Mary, 24 March p. 39/61 Dirac + Pauli moment

B. Lee Roberts, College of William and Mary, 24 March p. 40/61 Dirac Equation Predicts g=2 radiative corrections change g Schwinger

B. Lee Roberts, College of William and Mary, 24 March p. 41/61 The CERN Muon (g-2) Experiments The muon was shown to be a point particle obeying QED (Quantum Electrodynamics) The final CERN precision was 7.3 ppm

B. Lee Roberts, College of William and Mary, 24 March p. 42/61 Standard Model Value for (g-2) relative contribution of heavier things

B. Lee Roberts, College of William and Mary, 24 March p. 43/61 Lowest Order Hadronic from e + e - annihilation Cauchy’s theorem and the optical theorem

B. Lee Roberts, College of William and Mary, 24 March p. 44/61 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, College of William and Mary, 24 March p. 45/61 SUSY connection between a , D μ, μ → e

B. Lee Roberts, College of William and Mary, 24 March p. 46/61 Spin Precession Frequencies:  in B field

B. Lee Roberts, College of William and Mary, 24 March p. 47/61 If we use an electric quadrupole field for vertical focusing we get 0

B. Lee Roberts, College of William and Mary, 24 March p. 48/61 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, College of William and Mary, 24 March p. 49/61 muon (g-2) storage ring

B. Lee Roberts, College of William and Mary, 24 March p. 50/61

B. Lee Roberts, College of William and Mary, 24 March p. 51/61 Detectors and vacuum chamber Detector acceptance depends on radial position of the  when it decays.

B. Lee Roberts, College of William and Mary, 24 March p. 52/61

B. Lee Roberts, College of William and Mary, 24 March p. 53/61 Where we came from:

B. Lee Roberts, College of William and Mary, 24 March p. 54/61 Today with e + e - based theory: All E821 results were obtained with a “blind” analysis.

B. Lee Roberts, College of William and Mary, 24 March p. 55/61 Can we do better and confront theory more strongly? With a 2.7  discrepancy, you’ve got to go further. A new upgraded experiment to go from ±0.5 ppm to ± 0.2 ppm was approved by the BNL PAC in September 2004 It will be considered by the Particle Physics Project Prioritization Panel (P5) next Monday.

B. Lee Roberts, College of William and Mary, 24 March p. 56/61 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, College of William and Mary, 24 March p. 57/61 a μ implications for the muon EDM

B. Lee Roberts, College of William and Mary, 24 March p. 58/61 An EDM can also cause spin precession The EDM causes the spin to precess out of plane. The motional E - field, β X B, is much stronger than laboratory electric fields (MV/m)

B. Lee Roberts, College of William and Mary, 24 March p. 59/61 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 Needs muons

B. Lee Roberts, College of William and Mary, 24 March p. 60/61 Summary and Outlook The muon has provided us with much knowledge on how nature works. V-A, G F, induced weak couplings, lepton flavor conservation, a  a precision test of the SM New experiments on the horizon may 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, could also show up as a muon EDM, as well as in Lepton flavor violation in  decay.

B. Lee Roberts, College of William and Mary, 24 March p. 61/61 Like most science, this is a work in progress Stay tuned !

B. Lee Roberts, College of William and Mary, 24 March p. 62/61

B. Lee Roberts, College of William and Mary, 24 March p. 63/61 Two Hadronic Issues: Lowest order hadronic contribution Hadronic light-by-light

B. Lee Roberts, College of William and Mary, 24 March p. 64/61 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, College of William and Mary, 24 March p. 65/61 Hadronic light-by-light This contribution must be determined by calculation. the knowledge of this contribution limits knowledge of theory value. +/- Signs are Important!

B. Lee Roberts, College of William and Mary, 24 March p. 66/61 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, College of William and Mary, 24 March p. 67/61 Tests of CVC (A. H ö cker – ICHEP04)

B. Lee Roberts, College of William and Mary, 24 March p. 68/61 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, College of William and Mary, 24 March p. 69/61 PSI ( BR sensitivity) MEG will start running in 2006

B. Lee Roberts, College of William and Mary, 24 March p. 70/61 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, College of William and Mary, 24 March p. 71/61 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, College of William and Mary, 24 March p. 72/61 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

B. Lee Roberts, College of William and Mary, 24 March p. 73/61 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, College of William and Mary, 24 March p. 74/61 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, College of William and Mary, 24 March p. 76/61 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, College of William and Mary, 24 March p. 77/61 Improved transmission into the ring Inflector Inflector aperture Storage ring aperture E821 Closed EndE821 Prototype Open End

B. Lee Roberts, College of William and Mary, 24 March p. 78/61 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, College of William and Mary, 24 March p. 79/61 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, College of William and Mary, 24 March p. 80/61 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)