1. The Anomalous Magnetic Dipole Moment of the Muon
Lee Roberts
Department of Physics
Boston University
B. Lee Roberts, NuFact June 2008

2. 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, NuFact June 2008

3. 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, NuFact June 2008

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

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

6. Magnetic and Electric Dipole Moments
B. Lee Roberts, NuFact June 2008

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

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

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

10. 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, NuFact June 2008

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

12. 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, NuFact June 2008

13. First muon spin rotation experiment
B. Lee Roberts, NuFact June 2008

14. B. Lee Roberts, NuFact08 - 30 June 2008

15. 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, NuFact June 2008

16. Experimental Technique
xc ≈ 77 mm
b ≈ 10 mrad
B·dl ≈ 0.1 Tm
Target
25ns bunch of 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, NuFact June 2008

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

18. 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, NuFact June 2008

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

20. 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, NuFact June 2008

21. 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, NuFact June 2008

22. 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, NuFact June 2008

23. 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, NuFact June 2008

24. 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, NuFact June 2008

25. 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, NuFact June 2008

26. 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, NuFact June 2008

27. 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 ± 9.1.
See: arXiv: v1 [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, NuFact June 2008

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

29. 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, NuFact June 2008

30. 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, NuFact June 2008

31. 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, NuFact June 2008

32. 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, NuFact June 2008

33. 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, NuFact June 2008

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

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

36. 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, NuFact June 2008

37. 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

38. or perhaps we can use the fixed target area
B. Lee Roberts, NuFact June 2008

39. 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, NuFact June 2008

40. 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

41. Possible Extension of Hadron Hall
To G-2 beam line

42. 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, NuFact June 2008

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

44. 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, NuFact June 2008

45. 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, NuFact June 2008