Measuring WWZ and WWgamma coupling constants with Z-pole data

Triple gauge boson couplings between Z, gamma and the W boson are determined by exploiting their impact on radiative corrections to fermion-pair production in e+e- interactions at centre-of-mass energies near the Z-pole. Recent values of observables in the electroweak part of the Standard model are used to determine the four parameters epsilon_1, epsilon_2, epsilon_3 and epsilon_b. In a second step the results on the four epsilon parameters are used to determine the couplings Delta-g^1_Z and Delta-kappa_gamma. For a wide range of scales, these indirect coupling measurements are more precise than recent direct measurements at LEP 2 and at the TEVATRON. The Standard model predictions agree well with these measurements.Comment: 6 pages, 2 tables, 4 figure

Information Technology and Legal Ethics: Expanding the Teaching and Understanding of Legal Ethics Through the Creation of a New Generation of Electronic Reference Materials

Cramton and Martin present a very brief summary of the inward-looking elements of the Cornell Law School prorgam to improve the basic required course in professional ethics and to encourage the pervasive teaching of the subject throughout the law curriculum. The Cornell program focuses on the preparation and dissemination of electronic material on legal ethics on a state-by-state basis

Sobolev metrics on shape space of surfaces

Let $M$ and $N$ be connected manifolds without boundary with $\dim(M) < \dim(N)$, and let $M$ compact. Then shape space in this work is either the manifold of submanifolds of $N$ that are diffeomorphic to $M$, or the orbifold of unparametrized immersions of $M$ in $N$. We investigate the Sobolev Riemannian metrics on shape space: These are induced by metrics of the following form on the space of immersions: G^P_f(h,k) = \int_{M} \g(P^f h, k)\, \vol(f^*\g) where \g is some fixed metric on $N$, f^*\g is the induced metric on $M$, $h,k \in \Gamma(f^*TN)$ are tangent vectors at $f$ to the space of embeddings or immersions, and $P^f$ is a positive, selfadjoint, bijective scalar pseudo differential operator of order $2p$ depending smoothly on $f$. We consider later specifically the operator $P^f=1 + A\Delta^p$, where $\Delta$ is the Bochner-Laplacian on $M$ induced by the metric $f^*\bar g$. For these metrics we compute the geodesic equations both on the space of immersions and on shape space, and also the conserved momenta arising from the obvious symmetries. We also show that the geodesic equation is well-posed on spaces of immersions, and also on diffeomorphism groups. We give examples of numerical solutions.Comment: 52 pages, final version as it will appea

Pseudoriemannian metrics on spaces of bilinear structures

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation explicitly. Each space of pseudo Riemannian metrics with fixed signature is a geodesically closed submanifold. The space of non degenerate 2-forms is also a geodesically closed submanifold. Then we show that, if we fix a distribution on $M$, the space of all Riemannia metrics splits as the product of three spaces which are everywhere mutually orthogonal, for the usual metric. We investigate this situation in detail

Uniqueness of the Fisher-Rao metric on the space of smooth densities

MB was supported by ‘Fonds zur F¨orderung der wissenschaftlichen Forschung, Projekt P 24625’