The Anomalous Magnetic Dipole Moment m of the

The Anomalous Magnetic Dipole Moment m of the Muon Lee Roberts Department of Physics Boston University roberts @bu. edu http: //g 2 pc 1. bu. edu/~roberts B. Lee Roberts, Nu. Fact 08 - 30 June 2008 1

Outline m • Introduction to the muon • Magnetic (am ) and electric (dm ) dipole moments – E 821 result and the SM • Limits on CPT/Lorentz Violation in muon spin precession • Future improvements in am ? • Summary and conclusions. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 2

First published observation of the muon came from cosmic rays: Paul Kunze, m “a particle of uncertain nature” Z. Phys. 83, 1 (1933) B. Lee Roberts, Nu. Fact 08 - 30 June 2008 3

Muon properties: m • Born Polarized • Lifetime ~2. 2 ms, • mm/me = 206. 768. . • Decay is self-analyzing B. Lee Roberts, Nu. Fact 08 - 30 June 2008 4

Theory of Magnetic and Electric Dipole Moments m Proc. R. Soc. (London) A 117, 610 (1928) B. Lee Roberts, Nu. Fact 08 - 30 June 2008 5

Magnetic and Electric Dipole Moments B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 6

The magnetic dipole moment directed along spin. m 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, Nu. Fact 08 - 30 June 2008 7

Modern Notation: m • Muon Magnetic Dipole Momoment am chiral changing • Muon EDM B. Lee Roberts, Nu. Fact 08 - 30 June 2008 8

The SM Value for the muon anomaly (10 -10) m 10 (2) 11 659 178. 3 (4. 8) # from Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795– 881 B. Lee Roberts, Nu. Fact 08 - 30 June 2008 9

Since aμ represents a sum over all physics, it is sensitive to a wide range of potential new physics B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 10

aμ is sensitive to a wide range of new physics m • substructure • SUSY (with large tanβ ) • many other things (extra dimensions, etc. ) B. Lee Roberts, Nu. Fact 08 - 30 June 2008 11

Spin Motion in a Magnetic Field m Momentum turns with w. C, cyclotron frequency Spin turns with w. S Spin turns relative to the momentum with wa B. Lee Roberts, Nu. Fact 08 - 30 June 2008 12

First muon spin rotation experiment m B. Lee Roberts, Nu. Fact 08 - 30 June 2008 13

m B. Lee Roberts, Nu. Fact 08 - 30 June 2008 14

Subsequent (g-2) experiments measured the difference frequency, wa, between the spin and momentum precession m With an electric quadrupole field for vertical focusing: 0 B. Lee Roberts, Nu. Fact 08 - 30 June 2008 15

Experimental Technique m xc ≈ 77 mm 25 ns bunch of 5 X 1012 protons from AGS b ≈ 10 mrad Pions B·dl ≈ 0. 1 Tm Inflector p=3. 1 Ge. V/c (1. 45 T) Target • Muon polarization • Muon storage ring • injection & kicking • focus with Electric Quadrupoles • 24 electron calorimeters Injection orbit Central orbit Kicker Storage Modules ring R=711. 2 cm d=9 cm R R Electric Quadrupoles (thanks to Q. Peng) B. Lee Roberts, Nu. Fact 08 - 30 June 2008 b xc 16

muon (g-2) storage ring m Muon lifetime tm = 64. 4 ms (g-2) period ta = 4. 37 ms Cyclotron period t. C = 149 ns B. Lee Roberts, Nu. Fact 08 - 30 June 2008 17

To measure wa, we used Pb-scintillating fiber Figure of merit: calorimeters. 400 MHz digitizer gives t, E m Count number of e- with Ee ≥ 1. 8 Ge. V B. Lee Roberts, Nu. Fact 08 - 30 June 2008 18

We count high-energy electrons as a function of time. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 19

The ± 1 ppm uniformity in the average field is obtained with special shimming tools. m We can shim the dipole, 0. 5 ppm contours quadrupole sextupole independently B. Lee Roberts, Nu. Fact 08 - 30 June 2008 20

The magnetic field is measured and controlled using pulsed NMR and the free-induction decay. m • 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, Nu. Fact 08 - 30 June 2008 21

When we started in 1983, theory and experiment were known to about 10 ppm. m Theory uncertainty was ~ 9 ppm Experimental uncertainty was 7. 3 ppm B. Lee Roberts, Nu. Fact 08 - 30 June 2008 22

E 821 achieved 0. 5 ppm and the e+e- based theory is also at the 0. 6 ppm level. Difference is 3. 7 3. 4 ss m Md. RR=Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795 B. Lee Roberts, Nu. Fact 08 - 30 June 2008 23

If the electroweak contribution is left out of the standard-model value, we get a 5. 1 s difference. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 24

am helps constrain new physics m 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, Nu. Fact 08 - 30 June 2008 25

The Snowmass Points and Slopes give reasonable benchmarks to test observables with model predictions m . . . no matter where the final value lands! Muon g-2 is a powerful discriminator Expt Present Future? Model Version B. Lee Roberts, Nu. Fact 08 - 30 June 2008 26

am will help constrain the interpretation of LHC data, e. g. tan b and sgn m parameter m MSSM reference point SPS 1 a With these SUSY parameters, LHC gets tan b of 10. 22 ± 9. 1. See: ar. Xiv: 0705. 4617 v 1 [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, Nu. Fact 08 - 30 June 2008 27

Improved experiment and theory for am is important m MSSM reference point SPS 1 a With these SUSY parameters, LHC gets tan b of 10. 22 ± 9. 1. See: ar. Xiv: 0705. 4617 v 1 [hep-ph] m > 0 by > 6 s tan b to < 20% B. Lee Roberts, Nu. Fact 08 - 30 June 2008 28

Spin Frequencies: m in B field with MDM & EDM spin difference The motional E - field, β X B, is (~GV/m). 0 m frequency = ws - wc The EDM causes the spin to precess out of plane. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 29

Total frequency m 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, Nu. Fact 08 - 30 June 2008 30

We have looked for this vertical oscillation in 3 ways m • 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, Nu. Fact 08 - 30 June 2008 31

Future Improvements in am? m • 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, Nu. Fact 08 - 30 June 2008 32

The error budget for a new experiment represents a continuation of improvements already made during E 821 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. 31 0. 21 ≤ 0. 1 Statistical uncertainty (ppm) 4. 9 1. 3 0. 62 0. 66 ? Total Uncertainty (ppm) 5. 0 1. 3 0. 72 ≃0. 1 m • 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, Nu. Fact 08 - 30 June 2008 33

Possible Future Experiments ? m • Brookhaven – E 969 aimed for 0. 2 ppm overall error – No funding, most unlikely B. Lee Roberts, Nu. Fact 08 - 30 June 2008 34

muon (g-2) storage ring is at Brookhaven! Muon lifetime tm = 64. 4 ms (g-2) period ta = 4. 37 ms Cyclotron period t. C = 149 ns B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 35

Possible Future Experiments ? m • Brookhaven – E 969 aimed for 0. 2 ppm overall error – No funding, most unlikely • Fermilab – the m → e conversion experiment is top priority in the recent P 5 recommendations. – g-2 is mentioned as important, but with the three sites mentioned as possibilities. The Director is interested if the cost is ~ $20 M. – We would aim for 0. 1 ppm total error. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 36

Ideal conditions at FNAL using 8 Ge. V p n n Long beamline possible; more m, less flash High repetition rate of muon fills in ring m u 84 fills / 1. 4 sec 60 Hz 14. 5 x BNL u > 20 times statistics in one year Target where pbar target sits g-2 37

or perhaps we can use the fixed target area B. Lee Roberts, Nu. Fact 08 - 30 June 2008 m 38

Possible Future Experiments ? m • Brookhaven – E 969 aimed for 0. 2 ppm overall error – No funding, most unlikely • Fermilab – the m → e conversion experiment is top priority in the recent P 5 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, Nu. Fact 08 - 30 June 2008 39

J-PARC Facility (KEK/JAEA) m LINAC 3 Ge. V Synchrotoron Neutrino Beam to Kamioka Main Material and Life Science Facility Ring (30 Ge. V 50 G e. V) 2007 (JFY) 2008 (JFY) 2009 (JFY) Hadron Experimental Hall Bird’s eye photo in Feb. 2008 40 - p. 40/48

Possible Extension of Hadron Hall m To G-2 beam line 41 - p. 41/48

• • • m 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 theoretical front. We are actively exploring the future with FNAL and J-PARC B. Lee Roberts, Nu. Fact 08 - 30 June 2008 42

m THE END B. Lee Roberts, Nu. Fact 08 - 30 June 2008 43

R(s) measurements at low s m Babar/Belle (ISR) KLOE (ISR) VEPP-2000 VEPP-2 M At low s the cross-section is measured independently for each final state from Davier/Höcker B. Lee Roberts, Nu. Fact 08 - 30 June 2008 44

m The most important consequence of this work is indirect and confirms the known 3. 3 s discrepancy between the direct BNL measurement of the muon anomalous moment and its theoretical estimate relying on e+e- data. B. Lee Roberts, Nu. Fact 08 - 30 June 2008 45