The Anomalous Magnetic Dipole Moment of the Muon Lee Roberts Department of Physics Boston University roberts @bu.edu http://g2pc1.bu.edu/~roberts B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Outline Introduction to the muon Magnetic (am ) and electric (dm ) dipole moments E821 result and the SM Limits on CPT/Lorentz Violation in muon spin precession Future improvements in am ? Summary and conclusions. B. Lee Roberts, NuFact08 - 30 June 2008

First published observation of the muon came from cosmic rays: “a particle of uncertain nature” Paul Kunze, Z. Phys. 83, 1 (1933) B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Muon properties: Born Polarized Decay is self-analyzing Lifetime ~2.2 ms, mm/me = 206.768.. B. Lee Roberts, NuFact08 - 30 June 2008

Theory of Magnetic and Electric Dipole Moments Proc. R. Soc. (London) A117, 610 (1928) B. Lee Roberts, NuFact08 - 30 June 2008

Magnetic and Electric Dipole Moments B. Lee Roberts, NuFact08 - 30 June 2008

The magnetic dipole moment directed along spin. Dirac Theory: gs = 2 Dirac + Pauli moment For leptons, radiative corrections dominate the value of a ≃ 0.00116… e vrs. m : relative contribution of heavier things B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Modern Notation: Muon Magnetic Dipole Momoment am Muon EDM chiral changing B. Lee Roberts, NuFact08 - 30 June 2008

The SM Value for the muon anomaly (10-10) 10 (2) 11 659 178.3 (4.8) # from Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795–881 B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Since aμ represents a sum over all physics, it is sensitive to a wide range of potential new physics B. Lee Roberts, NuFact08 - 30 June 2008

aμ is sensitive to a wide range of new physics substructure SUSY (with large tanβ ) many other things (extra dimensions, etc.) B. Lee Roberts, NuFact08 - 30 June 2008

Spin Motion in a Magnetic Field Momentum turns with wC, cyclotron frequency Spin turns with wS Spin turns relative to the momentum with wa B. Lee Roberts, NuFact08 - 30 June 2008

First muon spin rotation experiment B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Subsequent (g-2) experiments measured the difference frequency, wa, between the spin and momentum precession With an electric quadrupole field for vertical focusing: B. Lee Roberts, NuFact08 - 30 June 2008

Experimental Technique xc ≈ 77 mm b ≈ 10 mrad B·dl ≈ 0.1 Tm Target 25ns bunch of 5 X 1012 protons from AGS Pions p=3.1GeV/c Inflector (1.45T) Injection orbit Muon polarization Muon storage ring injection & kicking focus with Electric Quadrupoles 24 electron calorimeters Central orbit Kicker Modules Storage ring R=711.2cm d=9cm xc R b Electric Quadrupoles (thanks to Q. Peng) B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 muon (g-2) storage ring Muon lifetime tm = 64.4 ms (g-2) period ta = 4.37 ms Cyclotron period tC = 149 ns B. Lee Roberts, NuFact08 - 30 June 2008

To measure wa, we used Pb-scintillating fiber calorimeters. Figure of merit: Count number of e- with Ee ≥ 1.8 GeV 400 MHz digitizer gives t, E B. Lee Roberts, NuFact08 - 30 June 2008

We count high-energy electrons as a function of time. B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 The ± 1 ppm uniformity in the average field is obtained with special shimming tools. We can shim the dipole, quadrupole sextupole independently 0.5 ppm contours B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 The magnetic field is measured and controlled using pulsed NMR and the free-induction decay. Calibration to a spherical water sample that ties the field to the Larmor frequency of the free proton wp. So we measure wa and wp B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 When we started in 1983, theory and experiment were known to about 10 ppm. Theory uncertainty was ~ 9 ppm Experimental uncertainty was 7.3 ppm B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 E821 achieved 0.5 ppm and the e+e- based theory is also at the 0.6 ppm level. Difference is 3.4s 3.7 s MdRR=Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795 B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 If the electroweak contribution is left out of the standard-model value, we get a 5.1 s difference. B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 am helps constrain new physics In a constrained minimal supersymmetric model, (g-2)m provides an independent constraint on the SUSY LSP (lightest supersymmetric partner) being the dark matter candidate. Historically muon (g-2) has played an important role in restricting models of new physics. It provides constraints that are independent and complementary to high-energy experiments. CMSSM calculation Following Ellis, Olive, Santoso, Spanos, provided by K. Olive B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 The Snowmass Points and Slopes give reasonable benchmarks to test observables with model predictions Muon g-2 is a powerful discriminator ... no matter where the final value lands! Expt Present Future? Model Version B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 am will help constrain the interpretation of LHC data, e.g. tan b and sgn m parameter MSSM reference point SPS1a With these SUSY parameters, LHC gets tan b of 10.22 ± 9.1. See: arXiv:0705.4617v1 [hep-ph] Even with no improvement, am will provide the best value for tan b and show m > 0 to > 3 s B. Lee Roberts, NuFact08 - 30 June 2008

Improved experiment and theory for am is important MSSM reference point SPS1a With these SUSY parameters, LHC gets tan b of 10.22 ± 9.1. See: arXiv:0705.4617v1 [hep-ph] m > 0 by > 6 s tan b to < 20% B. Lee Roberts, NuFact08 - 30 June 2008

Spin Frequencies: m in B field with MDM & EDM spin difference frequency = ws - wc The motional E - field, β X B, is (~GV/m). The EDM causes the spin to precess out of plane. B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 Total frequency w wa wh Plane of the spin precession tipped by the angle d Number above (+) and below (-) the midplane will vary as: B. Lee Roberts, NuFact08 - 30 June 2008

We have looked for this vertical oscillation in 3 ways 5-piece vertical hododscope in front of the calorimeters called an FSD 14 detector stations Much finer x-y hododscope called a PSD 5 detector stations Traceback straw tube array 1 station No significant oscillation was found The observed Dam is not from an EDM at the 2.2 s level *Coming soon to a preprint server near you B. Lee Roberts, NuFact08 - 30 June 2008

Future Improvements in am? Theory (strong interaction part) will improve. both lowest order, and light-by-light If money were no object, how well could the experiment be improved? The limit of our technique is between ~0.1 and 0.06 ppm. B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 The error budget for a new experiment represents a continuation of improvements already made during E821 Systematic uncertainty (ppm) 1998 1999 2000 2001 E??? Goal Magnetic field – wp 0.5 0.4 0.24 0.17 ≤0.1 Anomalous precession – wa 0.8 0.3 0.31 0.21 Statistical uncertainty (ppm) 4.9 1.3 0.62 0.66 ? Total Uncertainty (ppm) 5.0 0.73 0.72 ≃0.1 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 beam scraping scheme, lower thresholds, more complete digitization periods, better energy calibration B. Lee Roberts, NuFact08 - 30 June 2008

Possible Future Experiments ? Brookhaven E969 aimed for 0.2 ppm overall error No funding, most unlikely B. Lee Roberts, NuFact08 - 30 June 2008

muon (g-2) storage ring is at Brookhaven! Muon lifetime tm = 64.4 ms (g-2) period ta = 4.37 ms Cyclotron period tC = 149 ns B. Lee Roberts, NuFact08 - 30 June 2008

Possible Future Experiments ? Brookhaven E969 aimed for 0.2 ppm overall error No funding, most unlikely Fermilab the m → e conversion experiment is top priority in the recent P5 recommendations. g-2 is mentioned as important, but with the three sites mentioned as possibilities. The Director is interested if the cost is ~ $20M. We would aim for 0.1 ppm total error. B. Lee Roberts, NuFact08 - 30 June 2008

Ideal conditions at FNAL using 8 GeV p Long beamline possible; more m, less flash High repetition rate of muon fills in ring 84 fills / 1.4 sec  60 Hz  14.5 x BNL > 20 times statistics in one year Target where pbar target sits g-2

or perhaps we can use the fixed target area B. Lee Roberts, NuFact08 - 30 June 2008

Possible Future Experiments ? Brookhaven E969 aimed for 0.2 ppm overall error No funding, most unlikely Fermilab the m → e conversion experiment is top priority in the recent P5 recommendations. g-2 is mentioned as important, but with the three sites mentioned as possibilities. We would aim for 0.1 ppm total error. It could be done at FNAL, and we have received significant interest there. J-PARC Significant interest in moving the ring there. goal is ≤ 0.1 total error B. Lee Roberts, NuFact08 - 30 June 2008

J-PARC Facility (KEK/JAEA) 3 GeV Synchrotoron LINAC 2007 (JFY) 2008 (JFY) 2009 (JFY) Main Ring (30 GeV  50 GeV) Hadron Experimental Hall Material and Life Science Facility Neutrino Beam to Kamioka Bird’s eye photo in Feb. 2008

Possible Extension of Hadron Hall To G-2 beam line

B. Lee Roberts, NuFact08 - 30 June 2008 Summary The measurement of e- and m± magnetic dipole moments has been an important benchmark for the development of QED and the standard model of particle physics. The muon anomaly has been particularly valuable in restricting physics beyond the standard model, and will continue to do so in the LHC Era There appears to be a difference between am and the standard-model prediction at the 3.4 s level. Much activity continues on the theoretical front. We are actively exploring the future with FNAL and J-PARC B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 THE END B. Lee Roberts, NuFact08 - 30 June 2008

R(s) measurements at low s VEPP-2M Babar/Belle (ISR) KLOE (ISR) VEPP-2000 At low s the cross-section is measured independently for each final state from Davier/Höcker B. Lee Roberts, NuFact08 - 30 June 2008

B. Lee Roberts, NuFact08 - 30 June 2008 The most important consequence of this work is indirect and confirms the known 3.3s discrepancy between the direct BNL measurement of the muon anomalous moment and its theoretical estimate relying on e+e- data. B. Lee Roberts, NuFact08 - 30 June 2008