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

Collaboration

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

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.

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

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.

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

Muon storage ring

Some numbers about the experiment Magnetic field : 1.45 T p : 61.79MHz 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 — 500 ns beam kicked onto orbit 0 — 15 s beam scraping 15 — 40 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

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=3.183 345 39(10) W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

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 A394 349 (1997)

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.

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.

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.

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+ .

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.

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

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.

Blind analysis and result After two analyses of p had been completed, p /2π = 61 791 400(11) Hz (0.2ppm), and four analyses of a had been completed, a /2π = 229 073.59(15)(5) Hz (0.7ppm), separately and independently, the anomalous magnetic moment was evaluated, am-=11 659 214(8)(3) 10-10

History of the experimental measurements

Compare μ+ and μ− to test CPT CPT test : Combined result : am=11 659 208(6) 10-10

Standard model calculation of a a(SM)= a(QED) + a(weak) + a(had)* a(QED)=11 658 472.07(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.

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

Electroweak Contributions

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.

Evaluation of R M. Davier et al., hep-ph/0208177

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) = 696.15(5.7)(2.4) × 10-10 (HMNT) aμ(had,lo) = 694.8 (8.6) × 10-10 (GJ) S. Eidelman at DAФNE 2004

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/0208177 S. Eidelman at DAФNE 2004

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

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)  10-10 (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

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

Comparison of SM and experiment e+e− : aμ = 11 659 184.1 (7.2had,lo)(3.5lbl)(0.3QED+EW) × 10-10 : aμ = 11 659 200.4 (5.8had,lo)(3.5lbl)(0.3QED+EW) × 10-10 experimental result : am=11 659 208(6) 10-10 …including KLOE result e+e− : Δaμ = 23.9 (7.2had,lo)(3.5lbl)(6exp) × 10-10 (2.4 σ) : Δaμ = 7.6 (5.8had,lo)(3.5lbl)(6exp) × 10-10 (0.9 σ) F. Nguyen at DAФNE 2004

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

Conclusions Upgraded muon g-2 experiment is expected to reduce the Measurement of a−=11 659 214 (8)(3)×10-10(0.7 ppm) a− and a+ agree with each other as expected by CPT The combined result a=11 659 208(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