 B. Lee Roberts, KEK – 21 March p. 1/27 The Magnetic and Electric Dipole Moments of the Muon Lee Roberts for the muon g-2 collaboration Department of Physics Boston University

 B. Lee Roberts, KEK – 21 March p. 2/27 Outline Introduction to the muon Magnetic ( a  ) and electric ( d  ) dipole moments –E821 result and the SM –(new) E821 EDM limit Future improvements in a ,  d  Summary and conclusions.

 B. Lee Roberts, KEK – 21 March p. 3/27 Birth and death of the Muon Produced polarized Decay is self-analyzing

 B. Lee Roberts, KEK – 21 March p. 4/27 Magnetic and Electric Dipole Interactions Muon Magnetic Dipole Momoment a  Muon EDM chiral changing

 B. Lee Roberts, KEK – 21 March p. 5/27 The E-M dipole moments directed along spin. Dirac + Pauli moment e vrs.  : relative contribution of heavier things Dirac Theory: g s = 2 For leptons, radiative corrections dominate the value of a ≃ …

 B. Lee Roberts, KEK – 21 March p. 6/27 The SM Value # de Rafael, hep-ph arXiv: well knownsignificant work ongoing

 B. Lee Roberts, KEK – 21 March p. 7/27 a μ is sensitive to a wide range of new physics, e.g.SUSY difficult to measure at LHC

 B. Lee Roberts, KEK – 21 March p. 8/27 E821 at Brookhaven We explored future possibilities both at Fermilab and J-PARC. Proposed P989 at Fermilab The Experiment(s):

 B. Lee Roberts, KEK – 21 March p. 9/27 Momentum turns with  C, cyclotron frequency Spin turns with  S Spin turns relative to the momentum with  a Spin Motion in a Magnetic Field

 B. Lee Roberts, KEK – 21 March p. 10/27 Electric quadrupole field for vertical focusing 0

 B. Lee Roberts, KEK – 21 March p. 11/27 Inflector Kicker Modules Storage ring Central orbit Injection orbit Pions p=3.1GeV/c E821 Experimental Technique Muon polarization Muon storage ring injection & kicking focus with Electric Quadrupoles 24 electron calorimeters R=711.2cm d=9cm (1.45T) Electric Quadrupoles (thanks to Q. Peng) x c ≈ 77 mm  ≈ 10 mrad  ·d ℓ ≈ 0.1 Tm xcxc R R  Target 25ns bunch of 5 X protons from AGS

 B. Lee Roberts, KEK – 21 March p. 12/27 To measure  a, we used Pb-scintillating fiber calorimeters. Count number of e - with E e ≥ 1.8 GeV 400 MHz digitizer gives t, E N A NA 2 =0.4

 B. Lee Roberts, KEK – 21 March p. 13/27 The field is mapped and monitored with NMR

 B. Lee Roberts, KEK – 21 March p. 14/27 E821 achieved 0.54 ppm and the e + e - based theory is also at the 0.6 ppm level. Hint is 3.6  S-M = de Rafael, arXiv:

 B. Lee Roberts, KEK – 21 March p. 15/27 - p. 15/68 Model UED The Snowmass Points and Slopes give benchmarks to test observables with model predictions Future? Present Muon g-2 is a powerful discriminator... no matter where the final value lands!

 B. Lee Roberts, KEK – 21 March p. 16/27 Suppose the MSSM point SPS1a is realized and the paramaters are determined at LHC- sgn(  gives sgn(  ) LHC (Sfitter) Old g-2 New g-2   sgn (  ) difficult to obtain from the collider tan  poorly determined by the collider from D. Stöckinger

 B. Lee Roberts, KEK – 21 March p. 17/27 Electric Dipole Moment: P T If CPT is valid, an EDM would imply non-standard model CP. Transformation Properties

 B. Lee Roberts, KEK – 21 March p. 18/27 Muon EDM Measurement parasitic to a  measurement Measure upward-going vs. downward-going decay electrons vs. time with straw tube arrays E821 straw-tube array arXiv: v1 motional Electric Field Tipped precession plane → up-down oscillation (out of phase with  a )

 B. Lee Roberts, KEK – 21 March p. 19/27 E821 traceback Data: up-going / down-going tracks vs. time, (modulo the g-2 frequency): BNL traceback measurement was entirely statistics limited –expect ≃ X 100 improvement in new experiment (g-2) signal: # Tracks vs time, modulo g-2 period, in phase. EDM Signal: Average vertical angle modulo g-2 period. Out-of- phase by 90° from g-2; this is the EDM signal (g-2) EDM

 B. Lee Roberts, KEK – 21 March p. 20/27 The present EDM limits are orders of magnitude from the standard-model value ParticlePresent EDM limit (e-cm) SM value (e-cm) n future  exp to * arXiv: v1

 B. Lee Roberts, KEK – 21 March p. 21/ Left - Right MSSM  ~  Multi Higgs MSSM  ~ e EDM (e.cm) E. Hinds’ e-EDM experiment at Imperial College with YbF molecules is starting to explore this region Standard Model d e < 1.6 x e.cm Commins (2002) Excluded region (Tl atomic beam) with thanks to Ed Hinds n The SUSY CP problem! The strong CP problem! 199 Hg 

 B. Lee Roberts, KEK – 21 March p. 22/27 Dedicated  EDM Experiment (not at magic  ) 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, KEK – 21 March p. 23/27 Muon EDM Limits: Present and Future E821 Factory Need: NA 2 = for d  ≃ e ·cm new (g-2) ? PSI ?JPARC ? Dedicated storage rings

 B. Lee Roberts, KEK – 21 March p. 24/27 PSI storage ring by A. Streun

 B. Lee Roberts, KEK – 21 March p. 25/27 a μ implications for the muon EDM assuming same New Physics participates (recall that (  today =295(81)X ) following Feng et al, NPB613, 366(2001) Either d µ is of order 10 –22 e cm, or the CP phase is strongly suppressed! Figure assumes that

 B. Lee Roberts, KEK – 21 March p. 26/27 Connection between MDM, EDM and the lepton flavor violating transition moment  → e  → e → e MDM, EDM ~~ SUSY slepton mixing

 B. Lee Roberts, KEK – 21 March p. 27/27 The measurement of e ± and  ± magnetic dipole moments has been an important benchmark for the development of QED and the standard model of particle physics. There appears to be a difference between a  and the standard-model prediction at the ≃ 3.5  level. The muon anomaly has been particularly valuable in restricting models of physics beyond the standard model, and will continue to do so in the LHC Era Much activity continues on the theoretical front. A new limit on the muon EDM is now available An improved ( g - 2 )  experiment: a  4 X, d  100 X better than E821 is now proposed at Fermilab Summary

 B. Lee Roberts, KEK – 21 March p. 28/27 Thank you, THE END

 B. Lee Roberts, KEK – 21 March p. 29/27 muon (g-2) storage ring Muon lifetime t m = 64.4 ms (g-2) period t a = 4.37 ms Cyclotron period t C = 149 ns

 B. Lee Roberts, KEK – 21 March p. 30/27 Into the ring through the inflector magnet Open-end inflector x2 increase in transmission Kicker deflects beam onto orbit Improvements planned for pulse shape / magnitude Existing Prototype open ended 

 B. Lee Roberts, KEK – 21 March p. 31/27 The error budget for a new experiment represents a continuation of improvements already made during E821 Field improvements: better trolley and absolute calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware Precession improvements will involve new beam scraping scheme, lower thresholds, more complete digitization periods, better energy calibration Systematic uncertainty (ppm) P989 Goal Magnetic field –  p ≤ 0.7 Statistical uncertainty (ppm) Total Uncertainty (ppm) ≃ 0.14 Anomalous precession –  a ≤ 0.7

Polarized muons delivered and stored in the ring at the magic momentum, GeV/c n Uses 6/20 batches*  parasitic to program n Proton plan up to AP0 target is almost the same as for Mu2e n Uses the same target and lens as the present p-bar program n Modified AP2 line (+ quads) n New beam stub into ring n Needs simple building near cryo services *Can use all 20 if MI program is off

The 900-m long decay beam reduces the pion “flash” by x20 and leads to 6 – 12 times more stored muons per proton (compared to BNL) Stored Muons / POT Flash compared to BNL parameterFNAL/BNL p / fill0.25  / p 0.4  survive to ring 0.01  at magic P 50 Net0.05

The Precision Field: Systematic errors Why is the error 0.11 ppm? –That’s with existing knowledge and experience with R&D defined in proposal, it will get better Next (g-2)

 a Systematic Error Summary

What drives the detector choice? n Compact based on fixed space n Non-magnetic to avoid field perturbations Resolution is not critical for  a u Useful for pileup & gain monitoring u E821 “8%”; We propose 10% for tungsten-based calorimeter n Pileup depends on signal speed and shower separation u 4/5 events separated was goal u GEANT sim work in good shape Many more details and studies available. See also,

Benefits of a longer beamline n Reduced pions n Permits “forward” decays n Collects “all” muons n Eliminates “lost muon” systematic from muons born just prior to the ring

Ring relocation n Heavy-lift helicopters bring coils to a barge n Rest of magnet is a “kit” that can be trucked to and from the barge