Spin-2 Amplitudes in Black-Hole Evaporation

Quantum amplitudes for $s=2$ gravitational-wave perturbations of Einstein/scalar collapse to a black hole are treated by analogy with $s=1$ Maxwell perturbations. The spin-2 perturbations split into parts with odd and even parity. We use the Regge-Wheeler gauge; at a certain point we make a gauge transformation to an asymptotically-flat gauge, such that the metric perturbations have the expected falloff behaviour at large radii. By analogy with $s=1$, for $s=2$ natural 'coordinate' variables are given by the magnetic part $H_{ij} (i,j=1,2,3)$ of the Weyl tensor, which can be taken as boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the data on the initial surface $\Sigma_I$ to be exactly spherically-symmetric. The (large) Lorentzian proper-time interval between $\Sigma_I$ and $\Sigma_F$, measured at spatial infinity, is denoted by $T$. We follow Feynman's $+i\epsilon$ prescription and rotate $T$ into the complex: $T\to{\mid}T{\mid} \exp(-i\theta)$, for $0<\theta\leq\pi/2$. The corresponding complexified {\it classical} boundary-value problem is expected to be well-posed. The Lorentzian quantum amplitude is recovered by taking the limit as $\theta\to 0_+$. For boundary data well below the Planck scale, and for a locally supersymmetric theory, this involves only the semi-classical amplitude $\exp(iS^{(2)}_{\rm class}$, where $S^{(2)}_{\rm class}$ denotes the second-variation classical action. The relations between the $s=1$ and $s=2$ natural boundary data, involving supersymmetry, are investigated using 2-component spinor language in terms of the Maxwell field strength $\phi_{AB}=\phi_{(AB)}$ and the Weyl spinor $\Psi_{ABCD}=\Psi_{(ABCD)}$

R-values in Low Energy e^+e^- Annihilation

This presentation briefly summarizes the recent measurements of R-values in low energy e^+e^- annihilation. The new experiments aimed at reducing the uncertainties in R-values and performed with the upgraded Beijing Spectrometer (BESII) at Beijing Electron Positron Collider (BEPC) in Beijing and with CMD-2 and SND at VEEP-2M in Novosibirsk are reviewed and discussed.Comment: 17 pages, 10 figures, invited presentation at the XIX International Symposium on Lepton and Photon Interactions at High Energy, Stanford University, August 199

On the Hadronic Contribution to Light-by-light Scattering in gμ−2g_\mu-2

We comment on the theoretical uncertainties involved in estimating the hadronic effects on the light-by-light scattering contribution to the anomalous magnetic moment of the muon, especially based on the analysis and results of T. Kinoshita, B. Ni\v zi\'c, and Y. Okamoto, Phys.\ Rev.\ D31, 2108 (1985). From the point of view of an effective field theory and chiral perturbation theory, we suggest that the charged pion contribution may be better determined than has been appreciated. However, the neutral pion contribution needs greater theoretical insight before its magnitude can be reliably estimated.Comment: 9 pages, no figures, U. Michigan UM-TH-93-18. (Input phyzzm to compile.) Revised version has minor changes in text. To be published in Phys. Rev. D, Comments sectio

The implications of noninertial motion on covariant quantum spin

It is shown that the Pauli-Lubanski spin vector defined in terms of curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2 particles in noninertial motion along a curved trajectory. The possibility of detecting this violation in muon decay experiments is explored, where the noninertial contribution to the decay rate becomes large for muon beams with large momenta and trajectories with radius of curvature approaching the muon's Compton wavelength scale. A new spacelike spin vector is derived from the Pauli-Lubanski vector that satisfies Lorentz invariance for both inertial and noninertial motion. In addition, this spin vector suggests a generalization for the classification of spin-1/2 particles, and has interesting properties that are applicable for both massive and massless particles.Comment: REVTeX file; 7 pages; 2 figures; slightly revised with new abstract; accepted for publication in Classical and Quantum Gravit

Improved α4\alpha^4 Term of the Muon Anomalous Magnetic Moment

We have completed the evaluation of all mass-dependent $\alpha^4$ QED contributions to the muon $g-2$, or $a_\mu$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\alpha^4$ term $A_2^{(8)} (m_\mu / m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)} (m_\mu / m_e, m_\mu / m_\tau)$ is 0.0376 (1). The term $A_2^{(8)} (m_\mu / m_\tau)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_\mu$ is $116 584 719.58 (0.02)(1.15)(0.85) \times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\alpha^4$ and $\alpha^5$ terms and 0.85 is from the uncertainty in $\alpha$ measured by atom interferometry. This raises the Standard Model prediction by $13.9 \times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_\mu$. It is within the noise of current uncertainty ($\sim 100 \times 10^{-11}$) in the estimated hadronic contributions to $a_\mu$.Comment: Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PR

Wave energy absorption by a submerged air bag connected to a rigid float

A new wave energy device features a submerged ballasted air bag connected at the top to a rigid float. Under wave action, the bag expands and contracts, creating a reciprocating air flow through a turbine between the bag and another volume housed within the float. Laboratory measurements are generally in good agreement with numerical predictions. Both show that the trajectory of possible combinations of pressure and elevation at which the device is in static equilibrium takes the shape of an S. This means that statically the device can have three different draughts, and correspondingly three different bag shapes, for the same pressure. The behaviour in waves depends on where the mean pressure-elevation condition is on the static trajectory. The captured power is highest for a mean condition on the middle section.Comment: Revised version submitted to Proc R Soc

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

CP violation from noncommutative geometry

If the geometry of space-time is \nc, i.e. $[x_{\mu},x_{\nu}]=i \theta_{\mu \nu}$, then \nc \cpviolng effects may be manifest at low energies. For a \nc scale $\Lambda \equiv \theta^{-1/2} \leq 2 TeV$, \cpviol from \ncg is comparable to that from the Standard Model (SM) alone: the \nc contributions to $\epsilon$ and $\epsilon'/\epsilon$ in the $K$-system, may actually dominate over the Standard Model contributions. Present data permit \ncg to be the only source of \cpviol. Furthermore the most recent findings for g-2 of the muon are consistent with predictions from \ncg. If the geometry of space-time is \nc, $i.e.$ $[x_{\mu},x_{\nu}]=i \theta_{\mu \nu}$, then \nc \cpviolng effects may be manifest at low energies. For a \nc scale $\Lambda \equiv \theta^{-1/2} \leq 2 TeV$, \cpviol from \ncg is comparable to that from the Standard Model (SM) alone: the \nc contributions to $\epsilon$ and $\epsilon'/\epsilon$ in the K-system, may actually dominate over the Standard Model contributions. Present data permit \ncg to be the only source of \cpviol. Furthermore the most recent findings for g-2 of the muon are consistent with predictions from \ncg.Comment: fixed notation, corrected some typo

Sensitive Search for a Permanent Muon Electric Dipole Moment

We are proposing a new method to carry out a dedicated search for a permanent electric dipole moment (EDM) of the muon with a sensitivity at a level of 10^{-24} e cm. The experimental design exploits the strong motional electric field sensed by relativistic particles in a magnetic storage ring. As a key feature, a novel technique has been invented in which the g-2 precession is compensated with radial electric field. This technique will benefit greatly when the intense muon sources advocated by the developers of the muon storage rings and the muon colliders become available.Comment: 16 pages, 3 figures. Submitted for publication in Proceedings of the International Workshop on High Intensity Muon Sources (HIMUS99), KEK, Japan, December 1-4 199