Five-leg photon-neutrino interactions

In a first part, 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 $\gamma\nu\to\gamma\gamma \nu$ 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 in this effective theory the processes $\gamma\nu\to\gamma\gamma\nu$ and $\gamma\gamma\to\gamma{\nu}\bar\nu$ and show how to use the disagreement between two computations in the literature concerning the reaction the direct computation of the photon-neutrino five-leg processes in the Standard Model, discuss possible astrophysical implications of our results, and provide simple fits to the exact expressions.