Factorized distorted wave calculations for electron, neutrino, and BSM processes

Abstract

We point out that, under certain conditions, the nuclear currents that couple to vector bosons can be written as the trace of the product of two matrices. One contains `nucleon dynamics', e.g. form factors, the other contains the overlaps of nuclear wavefunctions. This factorized form may always be obtained and viewed as a `local' approximation, in which particle four-momenta that enter in the transition operator are fixed to their asymptotic values. We write the overlap matrix in a general form in terms of Dirac matrices. The current with arbitrary couplings to the nucleon can then be evaluated using standard trace identities. We show that this encompasses non-relativistic models as well. We have tabulated overlaps obtained in the relativistic distorted-wave impulse approximation, which can be used to compute the single-nucleon knockout cross section. We give a self-contained overview of the formulae. We discuss some properties of the overlap matrices which may be derived from general principles, and highlight differences with the commonly used plane-wave impulse approximation. The factorized form is attractive for (neutrino) event generators: it abstracts away the nuclear model and allows to easily modify couplings to the nucleon. This allows to consistently treat electron, neutrino and beyond Standard Model (BSM) processes.