The Magnetic and Electric Dipole Moments of the Muon Lee Roberts Department of Physics Boston University roberts @bu.edu http://g2pc1.bu.edu/~roberts B. Lee Roberts, Heidelberg 11 June 2008 -p. 154
Outline Introduction to the muon Magnetic (a ) and electric (d ) dipole moments E821 result and the SM (new) E821 EDM limit Limits on CPT/Lorentz Violation in muon spin precession Future improvements in a, d? Summary and conclusions. B. Lee Roberts, Heidelberg 11 June 2008 -p. 254
First published observation of the muon came from cosmic rays: Paul Kunze, a particle of uncertain nature Z. Phys. 83, 1 (1933) B. Lee Roberts, Heidelberg 11 June 2008 -p. 354
Identified in 1936 Study of cosmic rays by Seth Neddermeyer and Carl Anderson B. Lee Roberts, Heidelberg 11 June 2008 -p. 454
Muon properties: Lifetime ~2.2 s, practically forever 2 nd generation lepton m /m e = 206.768 277(24) produced polarized in-flight decay: both forward and backward muons are highly polarized Paul Scherrer Institut has 10 8 low-energy /s in a beam B. Lee Roberts, Heidelberg 11 June 2008 -p. 554
Death of the Muon Decay is self analyzing B. Lee Roberts, Heidelberg 11 June 2008 -p. 654
Theory of Magnetic and Electric Dipole Moments Proc. R. Soc. (London) A117, 610 (1928) B. Lee Roberts, Heidelberg 11 June 2008 -p. 754
Magnetic and Electric Dipole Moments B. Lee Roberts, Heidelberg 11 June 2008 -p. 854
The magnetic dipole moment directed along spin. Dirac Theory: g s = 2 Dirac + Pauli moment γ For leptons, radiative corrections dominate the value of a 0.00116 γ e vrs. : relative contribution of heavier things B. Lee Roberts, Heidelberg 11 June 2008 -p. 954
Modern Notation: Muon Magnetic Dipole Momoment a chiral changing Muon EDM B. Lee Roberts, Heidelberg 11 June 2008 - p. 1054
The SM Value for the muon anomaly (10-10 ) # from Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795 881 B. Lee Roberts, Heidelberg 11 June 2008 - p. 1154
Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics B. L. Roberts, Heidelberg 11 June 2008 - p. 12/54
a is sensitive to a wide range of new physics substructure B. Lee Roberts, Heidelberg 11 June 2008 - p. 1354
a is sensitive to a wide range of new physics ν substructure χ χ + γ χ 0 γ SUSY (with large tanβ ) many other things (extra dimensions, etc.) B. Lee Roberts, Heidelberg 11 June 2008 - p. 1454
Spin Motion in a Magnetic Field Momentum turns with ω C, cyclotron frequency Spin turns with ω S Spin turns relative to the momentum with ω a B. Lee Roberts, Heidelberg 11 June 2008 - p. 1554
First muon spin rotation experiment B. Lee Roberts, Heidelberg 11 June 2008 - p. 1654
First muon spin rotation experiment B. Lee Roberts, Heidelberg 11 June 2008 - p. 1754
B. Lee Roberts, Heidelberg 11 June 2008 - p. 1854
Subsequent (g-2) experiments measured the difference frequency, ω a, between the spin and momentum precession With an electric quadrupole field for vertical focusing: 0 B. Lee Roberts, Heidelberg 11 June 2008 - p. 1954
Experimental Technique 25ns bunch of 5 X 10 12 protons from AGS Target Pions p=3.1gev/c π Muon polarization Muon storage ring injection & kicking focus with Electric Quadrupoles 24 electron calorimeters ν Inflector B v Injection orbit Central orbit Storage Kicker ring Modules R=711.2cm d=9cm (1.45T) x c 77 mm b 10 mrad Β δλ 0.1 Tm R (thanks to Q. Peng) Electric Quadrupoles x B. Lee Roberts, Heidelberg 11 June 2008 - p. 2054 c R b
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, Heidelberg 11 June 2008 - p. 2154
To measure ω a, we used Pb-scintillating fiber calorimeters. 400 MHz digitizer gives t, E Count number of e - with E e 1.8 GeV B. Lee Roberts, Heidelberg 11 June 2008 - p. 2254
We count high-energy electrons as a function of time. B. Lee Roberts, Heidelberg 11 June 2008 - p. 2354
The ± 1 ppm uniformity in the average field is obtained with special shimming tools. inner coilthermal insulation We can shim the dipole, quadrupole sextupole independently wedge dipole correction coil pole piece pole bump beam region programmable current sheet fixed NMR probes outer coils YOKE inner coil g 2 Magnet in Cross Section ρ = 7112 mm B. Lee Roberts, Heidelberg 11 June 2008 - p. 2454
The ± 1 ppm uniformity in the average field is obtained with special shimming tools. 0.5 ppm contours B. Lee Roberts, Heidelberg 11 June 2008 - p. 2554
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 ω p. So we measure ω a and ω p B. Lee Roberts, Heidelberg 11 June 2008 - p. 2654
When we started in 1983, theory and experiment were known to about 10 ppm. Theory uncertainty was ~ 9 ppm (10 ppm) (9.4 ppm) CERN ~1983 CERN + Experimental uncertainty was 7.3 ppm 116 590 000 116 591 000 Theory 116 592 000 a 116 593 000 116 594 000 116 595 000 X 10 11 B. Lee Roberts, Heidelberg 11 June 2008 - p. 2754
E821 achieved 0.5 ppm and the e + e - based theory is also at the 0.6 ppm level. Difference is 3.4σ MdRR=Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795 B. Lee Roberts, Heidelberg 11 June 2008 - p. 2854
If the electroweak contribution is left out of the standard-model value, we get a 5.1 σ difference. B. Lee Roberts, Heidelberg 11 June 2008 - p. 2954
a helps constrain new physics In a constrained minimal supersymmetric model, (g-2) provides an independent constraint on the SUSY LSP (lightest supersymmetric partner) being the dark matter candidate. 800 tan β = 10, > 0 m 0 (GeV) scalar mass 700 600 500 400 300 200 100 m χ ± g-2 ± 1 ± 2 = 104 GeV m h = 114 GeV 0 100 200 300 400 500 600 700 800 900 1000 gaugino mass WMAP restrictions m 1/2 (GeV) 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, Heidelberg 11 June 2008 - p. 3054
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, Heidelberg 11 June 2008 - p. 3154
a will help constrain the interpretation of LHC data, e.g. tan β and sgn parameter MSSM reference point SPS1a With these SUSY parameters, LHC gets tan β of 10.22 ± 9.1. See: arxiv:0705.4617v1 [hep-ph] Even with no improvement, a will provide the best value for tan β and show > 0 to > 3 σ B. Lee Roberts, Heidelberg 11 June 2008 - p. 3254
Improved experiment and theory for a is important MSSM reference point SPS1a With these SUSY parameters, LHC gets tan β of 10.22 ± 9.1. See: arxiv:0705.4617v1 [hep-ph] > 0 by > 6 σ tan β to < 20% B. Lee Roberts, Heidelberg 11 June 2008 - p. 3354
Search for a Muon EDM B. Lee Roberts, Heidelberg 11 June 2008 - p. 3454
Electric Dipole Moment: P T Transformation Properties If CPT is valid, an EDM would imply non-standard model CP. B. Lee Roberts, Heidelberg 11 June 2008 - p. 3554
Purcell and Ramsey: EDM would violate Parity Proposed to search for an EDM of the neutron raises directly the question of parity. Phys. Rev. 78 (1950) B. Lee Roberts, Heidelberg 11 June 2008 - p. 3654
Spin Frequencies: in B field with MDM & EDM 0 The motional E - field, β X B, is (~GV/m). B. Lee Roberts, Heidelberg 11 June 2008 - p. 3754
Spin Frequencies: in B field with MDM & EDM 0 The motional E - field, β X B, is (~GV/m). (not to scale) The EDM causes the spin to precess out of plane. ω a ω η ω B β x B B. Lee Roberts, Heidelberg 11 June 2008 - p. 3854
Total frequency ω a ω Plane of the spin precession tipped by the angle δ ω η Number above (+) and below (-) the midplane will vary as: B. Lee Roberts, Heidelberg 11 June 2008 - p. 3954
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 Δa is not from an EDM at the 2.2 σ level *Coming soon to a preprint server near you B. Lee Roberts, Heidelberg 11 June 2008 - p. 4054
The present EDM limits are orders of magnitude from the standard-model value Particle Present EDM limit (e-cm) SM value (e-cm) n future exp 10-24 to 10-25 *final and will be submitted to PRD soon B. Lee Roberts, Heidelberg 11 June 2008 - p. 4154
e EDM (e.cm) 10-22 10-24 10-26 Multi Higgs Left - 199 10-28 Hg Right 10-30 10-32 10-34 n MSSM φ ~ 1 MSSM φ ~ α/π The SUSY CP problem! The strong CP problem! Excluded region (Tl atomic beam) Commins (2002) d e < 1.6 x 10-27 e.cm E. Hinds e-edm experiment at Imperial College with YbF molecules is starting to explore this region 10-36 Standard Model with thanks to Ed Hinds B. Lee Roberts, NuFact2008 4 July 2008 -p. 42/46
Dedicated EDM Experiment 0 Use a radial E-field to turn off the ω a precession With ω a = 0, the EDM causes the spin to steadily precess out of the plane. ω η B. Lee Roberts, Heidelberg 11 June 2008 - p. 4354
Muon EDM Limits: Present and Future E821 E821: G. Bennett, et al., (Muon g-2 collaboration) to be submitted to PRD 2008? new (g-2) ν Factory Need: NA 2 = 10 16 for d 10-23 e cm B. Lee Roberts, Heidelberg 11 June 2008 - p. 4454
Connection between MDM, EDM and the lepton flavor violating transition moment e SUSY slepton mixing ~ e ~ e ~ e B B ~ ~ MDM, EDM ~ ~ B. Lee Roberts, Heidelberg 11 June 2008 - p. 4554
An intermezzo: The search for CPT/Lorentz violation in muon spin precession B. Lee Roberts, Heidelberg 11 June 2008 - p. 4654
B. Lee Roberts, Heidelberg 11 June 2008 - p. 4754
What we measure that could show CPT/Lorentz violation 0 BUT Instead we have to use ω p is not affected to our level of sensitivity B. Lee Roberts, Heidelberg 11 June 2008 - p. 4854
CPT/Lorentz violation in the Lagrangian* a κ, b κ are CPT odd, others CPT even All terms violate Lorentz invariance In lowest-order, a is insensitive to violating terms *Bluhm, Kostelecký, Lane, PRL 84,1098 (2000) B. Lee Roberts, Heidelberg 11 June 2008 - p. 4954
Two tests of CPT/Lorentz violation: Difference between ω a for + and - Bennett, et al., Phys. Rev. D73, 072003-1 Sidereal time oscillation in ω a not seen: B. Lee Roberts, Heidelberg 11 June 2008 - p. 5054
The limits translate into 95% CL limits on parameters dividing by m Muonium hyperfine structure electron in a penning trap note that B. Lee Roberts, Heidelberg 11 June 2008 - p. 5154
Future Improvements in a? 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, Heidelberg 11 June 2008 - p. 5254
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 w p 0.5 0.4 0.24 0.17 0.1 Anomalous precession w a 0.8 0.3 0.31 0.21 0.1 Statistical uncertainty (ppm) 4.9 1.3 0.62 0.66? Total Uncertainty (ppm) 5.0 1.3 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, Heidelberg 11 June 2008 - p. 5354
Possible Future Experiments? Brookhaven E969 aimed for 0.2 ppm overall error No funding, most unlikely Fermilab the 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, Heidelberg 11 June 2008 - p. 5454
Summary 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. 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 a and the standard-model prediction at the 3.4 σ level. Much activity continues on the theoretical front. A new limit on the EDM is now available The experiment can certainly be improved... and we look forward to discussions with FNAL and J-PARC B. Lee Roberts, Heidelberg 11 June 2008 - p. 5554
THE END B. Lee Roberts, Heidelberg 11 June 2008 - p. 5654