Entropy and the variational principle for actions of sofic groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational principle in this context. In the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group C*-algebra.Comment: 44 pages; minor changes; to appear in Invent. Mat

Spin Resonance and dc Current Generation in a Quantum Wire

We show that in a quantum wire the spin-orbit interaction leads to a narrow spin resonance at low temperatures, even in the absence of an external magnetic field. Resonance absorption by linearly polarized radiation gives a dc spin current; resonance absorption by circularly polarized radiation gives a dc electric current or magnetization

Search for Lorentz and CPT Violation Effects in Muon Spin Precession

The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $\Delta\omega_{a}$ (=$\omega_{a}^{\mu^{+}}-\omega_{a}^{\mu^{-}}$); and a sidereal variation of $\omega_{a}^{\mu^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_{\mu}d_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{\mu^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{\mu^{-}} < 2.6 \times 10^{-24}$ GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to answer the referees suggestion

The Muon Anomalous Magnetic Moment and the Standard Model

The muon anomalous magnetic moment measurement, when compared with theory, can be used to test many extensions to the standard model. The most recent measurement made by the Brookhaven E821 Collaboration reduces the uncertainty on the world average of a_mu to 0.7 ppm, comparable in precision to theory. This paper describes the experiment and the current theoretical efforts to establish a correct standard model reference value for the muon anomaly.Comment: Plenary Talk; PANIC'02 XVI Particles and Nuclear International Conference, Osaka, Japan; Sept. 30 - Oct. 4, 2002; Report describes the published 0.7 ppm result and updates the theory statu

Improved Measurement of the Positive Muon Anomalous Magnetic Moment

A new measurement of the positive muon's anomalous magnetic moment has been made at the Brookhaven Alternating Gradient Synchrotron using the direct injection of polarized muons into the superferric storage ring. The angular frequency difference omega_{a} between the angular spin precession frequency omega_{s} and the angular orbital frequency omega_{c} is measured as well as the free proton NMR frequency omega_{p}. These determine R = omega_{a} / omega_{p} = 3.707~201(19) times 10^{-3}. With mu_{mu} / mu_{p} = 3.183~345~39(10) this gives a_{mu^+} = 11~659~191(59) times 10^{-10} (pm 5 ppm), in good agreement with the previous CERN and BNL measurements for mu^+ and mu^-, and with the standard model prediction.Comment: 4 pages, 4 figures. accepted for publication in Phys. Rev. D62 Rapid Communication

An Improved Limit on the Muon Electric Dipole Moment

Three independent searches for an electric dipole moment (EDM) of the positive and negative muons have been performed, using spin precession data from the muon g-2 storage ring at Brookhaven National Laboratory. Details on the experimental apparatus and the three analyses are presented. Since the individual results on the positive and negative muon, as well as the combined result, d=-0.1(0.9)E-19 e-cm, are all consistent with zero, we set a new muon EDM limit, |d| < 1.9E-19 e-cm (95% C.L.). This represents a factor of 5 improvement over the previous best limit on the muon EDM.Comment: 19 pages, 15 figures, 7 table

Search for Lorentz and CPT Violation Effects in Muon Spin Precession

The spin precession frequency of muons stored in the $(g-2)$ storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero $\Delta\omega_{a}$ (=$\omega_{a}^{\mu^{+}}-\omega_{a}^{\mu^{-}}$); and a sidereal variation of $\omega_{a}^{\mu^{\pm}}$. No significant effect is found, and the following limits on the standard-model extension parameters are obtained: $b_{Z} =-(1.0 \pm 1.1)\times 10^{-23}$ GeV; $(m_{\mu}d_{Z0}+H_{XY}) = (1.8 \pm 6.0 \times 10^{-23})$ GeV; and the 95% confidence level limits $\check{b}_{\perp}^{\mu^{+}}< 1.4 \times 10^{-24}$ GeV and $\check{b}_{\perp}^{\mu^{-}} < 2.6 \times 10^{-24}$ GeV.Comment: 5 pages, 3 figures, submitted to Physical Review Letters, Modified to answer the referees suggestion

Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a_mu = (g-2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a_mu(Expt) = 11 659 208.0(5.4)(3.3) x 10^-10, where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a_mu includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ~0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e+e- hadronic cross sections, lie 2.2 - 2.7 standard deviations below the experimental result.Comment: Summary paper of E821 Collaboration measurements of the muon anomalous magnetic moment, each reported earlier in Letters or Brief Reports; 96 pages, 41 figures, 16 tables. Revised version submitted to PR

News from the Muon (g-2) Experiment at BNL

The magnetic moment anomaly a_mu = (g_mu - 2) / 2 of the positive muon has been measured at the Brookhaven Alternating Gradient Synchrotron with an uncertainty of 0.7 ppm. The new result, based on data taken in 2000, agrees well with previous measurements. Standard Model evaluations currently differ from the experimental result by 1.6 to 3.0 standard deviations.Comment: Talk presented at RADCOR - Loops and Legs 2002, Kloster Banz, Germany, September 8-13 2002, to be published in Nuclear Physics B (Proc. Suppl.); 5 pages, 3 figure