1. Muon g-2 experimental results & theoretical developments
Huaizhang Deng
Yale University
University of Pennsylvania

2. Collaboration

3. Outline Overview of (g-2) Measure (g-2)μ in experiment
Principle of and experimental setup.
Analyses and results
Compare (g-2)+ and (g-2)−
Calculate (g-2) in theory
QED contribution
Weak contribution
Hadronic contribution
Conclusion

4. Magnetic dipole moment
The magnetic moment of a particle is related to its spin g
For Dirac pointlike particle : 
g=2
Anomalous magnetic moment
For the proton : ap1.8 because the proton is
composite particle.

5. g - 2  0 for the muon Largest contribution :
Some of other contributions :
hadronic
QED
weak
New physics ?

6. Why muon? proportional to m2. The muon is a point particle, so far.
(Hadrons, like p and n, are composite particles.)
The effects from heavy particles are generally
proportional to m2.
The muon lives long enough for us to measure.

7. Principle of the measurement
When =29.3 (p=3.09 Gev/c),
a is independent of E. a B

8. Muon storage ring

9. Some numbers about the experiment
Magnetic field : T p : MHz
Time scales :
149.2 ns cyclotron (or fast rotation) period c ,
4.4 s g-2 period a , what we want to measure
64.4 s dilated muon lifetime 
Experimental sequence :
t =0 beam injection
35 — ns beam kicked onto orbit
0 — s beam scraping
15 — s calorimeters gated on
15 — 1000 s g-2 measurement
33 ms beam injection repeats (12 times)
3 s circle repeats
3 day field measurement by trolley
1 year data-taking repeats
20 year whole experiment repeats

10. W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).
How to measure B
B is determined by measuring the proton nuclear
magnetic resonance (NMR) frequency p in the
magnetic field.
+/p= (10)
W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

11. NMR trolley 378 fixed probes around the ring 17 trolley probes
The NMR system is
calibrated against a
standard probe† of a
spherical water sample.
† X. Fei, V.W. Hughes, R. Prigl,
NIM A (1997)

12. Uniformity of the B field
The B field variation at the
center of the storage region.
<B>1.45 T
The B field averaged
over azimuth.

13. Stability of the B field
Calibration of the fixed
probe system with respect
to the trolley measurements
The magnetic field
measured by the fixed
probe system during
μ− run in 2001.

14. Systematic errors for p
Source of errors
Size [ppm]
μ μ−
Absolute calibration of standard probe
0.05
Calibration of trolley probe
0.15
0.09
Trolley measurements of B0
0.10
Interpolation with fixed probes
0.07
Uncertainty from muon distribution
0.03
Others†
Total
0.24
0.17
† higher multipoles, trolley temperature and voltage response,
eddy currents from the kickers, and time-varying stray fields.

15. How to measure a In the parity violated decay , e+ are emitted
preferentially along the muon spin direction in muon rest
frame. And e+ emitted along the muon momentum
direction get large Lorentz boost and have high energy in laboratory frame. Hence, a is determined by counting
the high energy e+ .

16. a data N(t)=Ne-t/[1-Acos(ωat+φ)] r(t)=Acos(ωat+φ)+(a/16)2
Divide N(t) into four independent
sets N1, N2, N3 and N4
r(t)=Acos(ωat+φ)+(a/16)2
Slow effects are largely
cancelled in the ratio method.

17. Coherent Betatron Oscillation
Cause :
Phase space not filled
Observation :
Beam centroid and
beam width oscillate
CBO phase varies from
0 to 2π around the ring
Solution :
Sum all detectors to
reduce the CBO effect

18. Error for a 0.11 Source of errors Size [ppm] μ+ μ-
μ μ-
Coherent betatron oscillation
0.21
0.07
Pileup
0.13
0.08
Gain changes
0.12
Lost muons
0.10
0.09
Binning and fitting procedure
0.06
Others†
Total systematic error
0.31
Statistical error
0.62
0.66
0.11
† AGS background, timing shifts, E field and vertical oscillations,
beam debunching/randomization.

19. Blind analysis and result
After two analyses of p had been completed,
p /2π = (11) Hz (0.2ppm),
and four analyses of a had been completed,
a /2π = (15)(5) Hz (0.7ppm),
separately and independently, the anomalous magnetic
moment was evaluated,
am-= (8)(3) 10-10

20. History of the experimental measurements

21. Compare μ+ and μ− to test CPT
CPT test :
Combined result :
am= (6) 10-10

22. Standard model calculation of a
a(SM)= a(QED) + a(weak) + a(had)*
a(QED)= (0.04)(0.1)10-10
a(weak)=15.1(0.1)(0.2)10-10
a(had,lo)=692.4(6.2)(3.6)10-10 *
a(had,nlo)=−98(0.1)10-10 *
a(had,lbl)=12(3.5)10-10 *
*The exact value and error of hadronic contribution are still under studies by
many groups.

23. QED contribution a(QED)=11 658 472.07(0.04)(0.1)10-10

24. Electroweak Contributions

25. Hadronic contribution (LO)
Cannot be calculated from pQCD alone
because it involves low energy scales
near the muon mass.
However, by dispersion theory,
this a(had,1) can be related to
measured in e+e- collision
or indirectly in  decay.

26. Evaluation of R
M. Davier et al., hep-ph/

27. aμ(had, lo) based on e+e− data
5.45
37.96±1.02±0.31 ω
100.0
696.3±6.2±3.6
Total
1.42
9.88±0.11±0.00
> 5.0
1.07
7.44±0.38±0.00
J/ψ,ψ’
4.87
33.92±1.72±0.03
2.0 − 5.0
9.07
63.18±2.19±0.86
0.6 − 2.0
5.13
35.71±0.84±0.20 φ
72.99
508.20±5.18±2.74 2π %
(DEHZ)
aμ(had,lo) = (5.7)(2.4) × (HMNT)
aμ(had,lo) = (8.6) × (GJ)
S. Eidelman at DAФNE 2004

28. Discrepancy between e+e− and  data
mode
e−e+ 
Δ(e−e+ − )
π−π+
508.20±5.18±2.74
520.06±3.36±2.62
-11.9±6.9
π−π+ 2π0
16.76±1.31±0.20
21.45±1.33±0.60
-4.7±1.8
2π−2π+
14.21±0.87±0.23
12.35±0.96±0.40
1.9±2.0
total
539.17±5.41±3.17
553.86±3.74±3.02
-14.7±7.9
aμ(had,lo) = 711.0(5.0)(0.8)(2.8)×10-10 (DEHZ)
M. Davier et al., hep-ph/
S. Eidelman at DAФNE 2004

29. Possible reasons for discrepancy
Problem with experimental data
Problem with SU(2) breaking corrections
Non-(V−A) contribution to weak interaction
Difference in mass of ρ mesons (mρ±>mρ0).
Current data indicate equality within a few MeV

30. Comparsion between CMD-2 and KLOE
Radiative return is another way to
measure hadronic contributions
Kloe
CMD-2
KLOE
(375.6  0.8stat  4.9syst+theo)  (1.3%)
only statistical
errors are shown
CMD-2
(378.6  2.7stat  2.3syst+theo)  10-10(0.9%)
Two measurements are in agreement
F. Nguyen at DAФNE 2004

31. Higher order hadronic contributions
a(had,nlo)=10.0(0.6)10-10
a(had,lbl)=8.6(3.5)10-10
a(had,lbl)=12.0(3.5)10-10
a(had,lbl)=13.6(2.5)10-10

32. Comparison of SM and experiment
e+e− :
aμ = (7.2had,lo)(3.5lbl)(0.3QED+EW) × 10-10 :
aμ = (5.8had,lo)(3.5lbl)(0.3QED+EW) × 10-10
experimental result : am= (6) 10-10
…including
KLOE result
e+e− :
Δaμ = (7.2had,lo)(3.5lbl)(6exp) × (2.4 σ) :
Δaμ = (5.8had,lo)(3.5lbl)(6exp) × (0.9 σ)
F. Nguyen at DAФNE 2004

33. Beyond standard model compositeness for leptons or gauge bosons.
extra dimensions, or extra particles,
particularly supersymmetric particles

34. Conclusions Upgraded muon g-2 experiment is expected to reduce the
Measurement of a−= (8)(3)×10-10(0.7 ppm)
a− and a+ agree with each other as expected by CPT
The combined result a= (6) ×10-10(0.5 ppm)
a(exp)−a(SM) is 2.4σ (e+e−) or 0.9σ ()
The discrepancy between e+e− and  data is confirmed by
KLOE
Upgraded muon g-2 experiment is expected to reduce the
experimental error to 0.2 ppm.
Efforts on solving discrepancy between e+e− and , and
attempts to calculate a(had) from lattice QCD