Huaizhang Deng Yale University Precise measurement of (g-2)  University of Pennsylvania

Collaboration

Prof. Vernon W. Hughes (1921  2003)

Outline What is (g-2)  and why we measure it ? Preliminary result of muon electric dipole moment. Analysis and result from the 2000 run. Principle of and experimental setup for the measurement. Theory of (g-2)  and its new development. Conclusions.

What is g-2 The magnetic moment of a particle is related to its spin g For Dirac pointlike particle :  g=2 For the proton : a p  1.8 because the proton is composite particle. Anomalous magnetic moment

g - 2  0 for the muon Largest contribution : Other standard model contributions : QED hadronic weak Contribution from new physics : a  (exp)-a  (SM)=a  (new physics)

Why muon? The muon is a point particle, so far. (Hadrons, like p and n, are composite particles.) The muon lives long enough for us to measure. The effects from heavy particles are generally proportional to m 2.

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

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).

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 +.

Muon storage ring

Some numbers about the experiment Time scales : nscyclotron (or fast rotation) period  c, 4.4  sg-2 period  a, what we want to measure 64.4  s dilated muon lifetime  Experimental sequence : t =0 beam injection Magnetic field : 1.45 T  p : 61.79MHz 35 — 500 ns beam kicked onto orbit 0 — 15  s beam scraping 5 — 40  s calorimeters gated on 45 — 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

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

Trolley measurement The B field variation at the center of the storage region.  1.45 T The B field averaged Over azimuth.

Fixed probe measurements Calibration of the fixed probe system with respect to the trolley measurements The magnetic field measured by the fixed probe system during 2000 run.

Systematic errors for  p Source of errorsSize [ppm] Absolute calibration of standard probe0.05 Calibration of trolley probe Trolley measurements of B Interpolation with fixed probes Inflector fringe field Uncertainty from muon distribution Others† Total † higher multipoles, trolley temperature and voltage response, eddy currents from the kickers, and time-varying stray fields.

2000  a data

Coherent betatron oscillation (cbo) kick

CBO effect on ω a

Cancellation of cbo around the ring CBO effect shown on the average energy of e + Cancellation of cbo effect after summing all detector together.

Error for  a Source of errorsSize [ppm] Coherent betatron oscillation Pileup0.13 Gain changes Lost muons0.10 Binning and fitting procedure AGS background0.10 Others†0.06 Total systematic error Statistical error † Timing shifts, E field and vertical oscillations, beam debunching/randomization.

Blind analysis and result After two analyses of  p had been completed,  p = (15) Hz (0.2ppm), and four analyses of  a had been completed,  a = (14)(7) Hz (0.7ppm), separately and independently, the anomalous magnetic moment was evaluated, a  = (7)(5) 

Standard model calculation of a  a  (SM)= a  (QED)+ a  (had)+ a  (weak) a  (QED)= (0.29)  (0.025 ppm) a  (weak)=15.1(0.4)  (0.03 ppm) Both QED and weak contribution has been calculated to high accuracy. The accuracy of a  (had) is about 0.6 ppm.

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

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

Comparison between e + e - and  M. Davier et al., hep-ph/ M. Davier et al., hep-ph/

Experimental and theoretical values

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

Muon electric dipole moment s ω obs ω edm ωaωa δ Vertical profile of decay positrons oscillates with frequency of g-2 with phase 90 o different from g-2 phase with amplitude proportional to d μ where

Amplitude with CBO frequency [μm] Amplitude with g-2 frequency [μm] Preliminary result of muon EDM d μ =(−0.1±1.4)× e·cm d μ < 2.8× e·cm (95% CL)

Conclusions Improve the accuracy of a  to 0.7 ppm The discrepancy between a  (exp) and a  (SM) is , depending on theory. Uncertainty is about half the size of the weak contribution. We are analyzing the data for negative muons, a test of CPT. Factor 3.75 improvement on the upper limit of muon electric dipole moment.

Superconducting inflector The radial phase space allowed by the inflector aperture (green) is smaller than that allowed by the storage ring (red).

Photo of the storage ring inflector kickers Detectors

Magnet

Muon distribution Radial muon distribution determined by the Fourier trans- formation of cyclotron periods when beam is debunching. Vertical muon distribution is symmetric.

Residual after fit with ideal function

Detectors and positron signals

Polarized muons Parity violated decay produces longitudinally polarized muons.  +  + s p  : spin 0 : left handed  : left handed

Half ring effect due to cbo

Pileup correction real pileup : |  t|<2.9 ns constructed pileup : |  t-10|<2.9 ns raw corrected raw corrected later time

Muon loss Absolute normalization is determined by fit.

Evaluation of R (low energy region) M. Davier et al., hep-ph/

a  (had,1)

a  (had,lbl)=8.6(3.5)  Higher order hadronic contributions a  (had,2)=10.1(0.6) 

Near future Analysis of 2001 data on   with reduced systematic error and roughly the same statistical error. Test CPT. Assuming CPT, reduce the total statistical error. Measurement of muon electric dipole moment. Muon life time measurement. Sidereal day variation of a . Theoretical evaluation continues to be scrutinized. Radiative return data from KLOE and B factory. Lattice QCD calculation.