Equivariant K-homology for some Coxeter groups

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter cells. Our calculations amount to the K-theory of the reduced C^*-algebra of W, via the Baum-Connes assembly map.Comment: 22 pages, 5 figure

K-theory for group C*-algebras

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjectur

Vus and neutron beta decay

We discuss the effect of the recent change of $V_{\rm us}$ by three standard deviations on the standard model predictions for neutron beta decay observables. We also discuss the effect the experimental error bars of $V_{\rm us}$ have on such predictions. Refined precision tests of the standard model will be made by a combined effort to improve measurements in neutron beta decay and in strangeness-changing decays. By itself the former will yield very precise measurements of $V_{\rm ud}$ and make also very precise predictions for $V_{\rm us}$

Finite width induced modification to the electromagnetic form factors of spin-1 particles

The inclusion of the unstable features of a spin-1 particle, without breaking the electromagnetic gauge invariance, can be properly accomplished by including higher order contributions as done in the so-called fermion loop scheme (for the W gauge boson), and the boson loop scheme (for vector mesons). This induces a non trivial modification to the electromagnetic vertex of the particle, which must be considered in addition to any other contribution computed as stable particles. Considering the modified electromagnetic vertex, we obtain general expressions for the corresponding corrections to the multipoles as a function of the mass of the particles in the loop. For the W gauge boson no substantial deviations from the stable case is observed. For the rho and K* mesons the mass of the particles in the loop makes a significant effect, and can be comparable with corrections of different nature .Comment: 11 pages, 1 figure. Extended discussion, main equations rewritten to exhibit limiting behavior. Results for K* meson added. Accepted for publication in PR