New resonances with masses of order a few ${rm TeV}$ might be discovered at the LHC. We show that no resonance that couples to electrons only through Standard Model interactions can decay to both $e^+e^-$and $gamma gamma$ with significant branching r
atios. This means that finding both electron-positron and two-photon final states is evidence that electrons couple directly to the new physics associated with the resonance and furthermore that the resonance is not spin-1. The least fine-tuned such examples involve electron compositeness. One such example, Kaluza Klein excitations of the graviton in the version of the Randall Sundrum Model where Standard Model matter is located on the ${rm TeV}$ brane, can be distinguished from other possibilities by its predicted branching fractions into the two modes.
First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations are small
, i.e., of order a few percent, but nonetheless including correlations is very important, for managing portfolio credit risk and pricing some credit derivatives (e.g. first to default baskets). In first passage models the exact dependence of the joint survival probability of more than two firms on their asset correlations is not known. We derive an expression for the dependence of the joint survival probability of $n$ firms on their asset correlations using first order perturbation theory in the correlations. It includes all terms that are linear in the correlations but neglects effects of quadratic and higher order. For constant time independent correlations we compare the first passage model expression for the joint survival probability with what a multivariate normal Copula function gives. As a practical application of our results we calculate the dependence of the five year joint survival probability for five basic industrials on their asset correlations.
