Inelastic photon-neutrino interactions using an effective Lagrangian

Abstract

We justify the feasibility of substituting a photon leg by a neutrino current in the Euler-Heisenberg Lagrangian to obtain an effective Lagrangian for the process $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\nu}$ and its crossed reactions. We establish the link between these processes and the four-photon scattering in both the standard model and the effective theory. As an application, we compute the processes $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\nu}$ and $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\gamma}\ensuremath{\nu}\overline{\ensuremath{\nu}},$ give their polarized cross sections, and show how to use the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\gamma}\ensuremath{\gamma}$ results as a check. We settle the question about the disagreement between two computations in the literature concerning the reaction $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\gamma}\ensuremath{\nu}\overline{\ensuremath{\nu}}.$