B. Lee Roberts, SPIN2004 –Trieste -11 September p. 1/54 New Results on Muon (g-2) Past, Present and Future Experiments B. Lee Roberts Department of Physics Boston University

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 2/54 The g-2 Collaboration Boston University, Brookhaven National Laboratory, Budker Institute, Cornell University, University of Heidelberg ( * KVI), University of Illinois, KEK, University of Minnesota, Tokyo Institute of Technology, Yale University Vernon W. Hughes

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 3/54 Outline Prehistory: Stern to CERN Theory of Muon (g-2) E821: from 7.3 ppm to 0.5 ppm The Future: E969 from 0.5 to 0.20 ppm Summary and Outlook

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 4/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 5/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 6/54 (in modern language)

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 7/54 Dirac + Pauli moment

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 8/54 Dirac Equation Predicts g=2 radiative corrections change g

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 9/54 The Lowest Order Radiative Corrections The vertex correction:

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 10/54 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, SPIN2004 –Trieste -11 September p. 11/54 MDM (g-2) chirality changing EDM Matrix Element for MDM and EDM

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 12/54 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, SPIN2004 –Trieste -11 September p. 13/54 Standard Model Value for (g-2)

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 14/54 Two Hadronic Issues: Lowest order hadronic contribution Hadronic light-by-light

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 15/54 Lowest Order Hadronic from e + e - annihilation

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 16/54 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, SPIN2004 –Trieste -11 September p. 17/54 a(had) from hadronic  decay? Must assume CVC, no second-class currents, make the appropriate isospin breaking corrections. decay has no isoscalar piece, while e + e - does Let’s look at the branching ratio and F π from the two data sets:

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 18/54 Tests of CVC (A. Höcker – ICHEP04)

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 19/54 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, SPIN2004 –Trieste -11 September p. 20/54 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, SPIN2004 –Trieste -11 September p. 21/54 A. Höcker at ICHEP04

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 22/54 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, SPIN2004 –Trieste -11 September p. 23/54 Hadronic light-by-light This contribution must be determined by calculation. the knowledge of this contribution limits knowledge of theory value.

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 24/54 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, SPIN2004 –Trieste -11 September p. 25/54 SUSY connection between a , D μ, μ → e

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 26/54 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

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 27/54 Current Discrepancy Standard Model The CMSSM plot with error on  a  of 4.6 x (assuming better theory and a new BNL g-2 experiment)  a  =24(4.6) x (discrepancy at 6   a   0 (4.6) x

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 28/54 Spin Precession Frequencies: 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

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 29/54 Inflector Kicker Modules Storage ring Ideal 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 

The field values along the muon trajectory are measured several times per week with 17 NMR probes mounted on a trolley. The field is tracked continually with ~160 out of 375 NMR probes in the top and bottom walls of the vacuum chamber. The system is calibrated in situ against a standard* before and after data taking with beam Experiment - Field Measurement (I) calibration uncertainties (II) measurement uncertainties (III) interpolation uncertainties (IV) apparatus response and field perturbations (IV)

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 31/54 muon (g-2) storage ring

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 32/54 Field Shimming Source of UncertaintySource of Uncertainty Absolute CalibrationAbsolute Calibration Calibration of TrolleyCalibration of Trolley Trolley Measurements of B0Trolley Measurements of B Interpolation with the fixed probesInterpolation with the fixed probes Inflector fringe fieldInflector fringe field uncertainty from muon distributionuncertainty from muon distribution Other*Other* TotalTotal * higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time-varying stray fields. * higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time-varying stray fields. (I)(I) (II)(II) (III)(III) (IV)(IV) 2001

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 33/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 34/54 Magnetic Field Uncertainty Systematic uncertainty (ppm) Magnetic field –  p

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 35/54 Beam Dynamics mismatch between entrance channel and storage volume, + imperfect kick causes coherent beam oscillations beam storage region

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 36/54 Coherent Betatron Oscillations 2  is one turn around the ring

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 37/54 Frequencies in the g-2 Ring

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 38/54 Detectors and vacuum chamber

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 39/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 40/54 Fourier Transform: residuals to 5-parameter fit beam motion across a scintillating fiber – ~15 turn period

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 41/54 Effects of the CBO on e - spectrum CBO causes modulation of N, amplitude ~0.01 CBO causes modulation of observed energy distribution which in turn causes oscillation in A(E),  (E), with amplitudes ~0.001, ~1 mrad.

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 42/54 Functional form of the time spectrum A 1 and A 2 → artificial shifts in  a up to 4 ppm in individual detectors when not accounted for.

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 43/54 Other Systematic Effects:  a muon losses gain changes and pedistal shifts pulse pileup

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 44/54 Muon Frequency Error Systematic uncertainty (ppm) Spin precession –  a

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 45/54 Where we came from:

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 46/54 Today with e + e - based theory: All E821 results were obtained with a “blind” analysis.

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 47/54 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 ppp –lower systematic errors –more beam

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 48/54 Strategy of the improved experiment More muons – E821 was statistics limited  stat = 0.46 ppm,  syst = 0.3 ppm –Backward-decay, higher-transmission beamline –New, open-end inflector –Upgrade detectors, electronics, DAQ Improve knowledge of magnetic field B –Improve calibration, field monitoring and measurement Reduce systematic errors on ω a –Improve the electronics and detectors –New parallel “integration” method of analysis

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 49/54 Improved transmission into the ring Inflector Inflector aperture Storage ring aperture E821 Closed EndP969 Proposed Open End

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 50/54 Pedestal vs. Time Near sideFar side E821: forward decay beam GeV/c Decay GeV/c This baseline limits how early we can fit data

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 51/54 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

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 52/54 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, SPIN2004 –Trieste -11 September p. 53/54 Summary g-2 continues to be at the center of interest in particle physics. E821 reached 0.5 ppm precision with a 2.7  discrepancy with SM –using e+e- data for the hadronic piece E969 has scientific approval, physics reach is x 2 to 2.5 over E821. Should clarify comparison with SM. (still need $)

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 54/54 Outlook Scenario 1 –LHC finds SUSY –(g-2) helps provide information on important aspects of this new reality, e.g. 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 !

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 55/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 56/54

B. Lee Roberts, SPIN2004 –Trieste -11 September p. 57/54 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, SPIN2004 –Trieste -11 September p. 58/54 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