Electromagnetic penguin operators and direct CP violation in K --> pi l^+ l^-

Supersymmetric extensions of the Standard Model predict a large enhancement of the Wilson coefficients of the dimension-five electromagnetic penguin operators affecting the direct CP violation in K_L --> pi^0 e^+ e^- and the charge asymmetry in K^\pm --> pi^\pm l^+ l^-. Here we compute the relevant matrix elements in the chiral quark model and compare these with the ones given by lattice calculationsComment: 12 pages, JHEP style, gluonic corrections to B_T adde

Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor is it the point where the input beam mode in the cavity is maximized.Comment: Eight pages in two-column format. Six color figures. To be published JOSA

Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent the unperturbed intracavity field anywhere in the detector as a linear combination of basis functions related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take great care to preserve numerically the nearly ideal longitudinal phase resonance conditions that would otherwise be provided by an external servo-locking control system. We have included the effects of nonlinear thermal focusing due to power absorption in both the substrates and coatings of the mirrors and beamsplitter, the effects of a finite mismatch between the curvatures of the laser wavefront and the mirror surface, and the diffraction by the mirror aperture at each instance of reflection and transmission. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare the resulting computations of intracavity fields in two special cases with those of a fast Fourier transform field propagation model. Additional systematic perturbations (e.g., mirror tilt, thermoelastic surface deformations, and other optical imperfections) can be included easily by incorporating the appropriate operators into the transfer matrices describing reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA

On the Analytic Structure of a Family of Hyperboloidal Beams of Potential Interest for Advanced LIGO

For the baseline design of the advanced Laser Interferometer Gravitational-wave Observatory (LIGO), use of optical cavities with non-spherical mirrors supporting flat-top ("mesa") beams, potentially capable of mitigating the thermal noise of the mirrors, has recently drawn a considerable attention. To reduce the severe tilt-instability problems affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror configuration, K. S. Thorne proposed a nearly-concentric mirror configuration capable of producing the same mesa beam profile on the mirror surfaces. Subsequently, Bondarescu and Thorne introduced a generalized construction that leads to a one-parameter family of "hyperboloidal" beams which allows continuous spanning from the nearly-flat to the nearly-concentric mesa beam configurations. This paper is concerned with a study of the analytic structure of the above family of hyperboloidal beams. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation between two generic hyperboloidal beams is investigated. This leads to a generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations. Possible implications and perspectives for the advanced LIGO optical cavity design are discussed.Comment: 9 pages, 6 figures, typos corrected, Eqs. (24) and (26) change

Kaon decay interferometry as meson dynamics probes

We discuss the time dependent interferences between $K_L$ and $K_S$ in the decays in $3\pi$ and $\pi\pi\gamma$, to be studied at interferometry machines such as the $\phi$-factory and LEAR. We emphasize the possibilities and the advantages of using interferences, in comparison with width measurements, to obtain information both on $CP$ conserving and $CP$ violating amplitudes. Comparison with present data and suggestions for future experiments are made.Comment: 15 pages, in RevTex, Report INFNNA-IV-93-31, UTS-DFT-93-2

Normal metal tunnel junction-based superconducting quantum interference proximity transistor: the N-SQUIPT

We report the fabrication and characterization of an alternative design for a superconducting quantum interference proximity transistor (SQUIPT) based on a normal metal (N) probe. The absence of direct Josephson coupling between the proximized metal nanowire and the N probe allows us to observe the full modulation of the wire density of states around zero voltage and current \textit{via} the application of an external magnetic field. This results into a drastic suppression of power dissipation which can be as low as a few $\sim 10^{-17}$ W. In this context the interferometer allows an improvement of up to four orders of magnitude with respect to earlier SQUIPT designs, and makes it ideal for extra-low power cryogenic applications. In addition, the N-SQUIPT has been recently predicted to be the enabling candidate for the implementation of coherent caloritronic devices based on proximity effect.Comment: 5 pages, 4 color figure

The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra