  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
$\gamma\gamma\to\gamma\gamma$ results as a check. We settle the question of the
disagreement between two computations in the literature concerning the reaction
$\gamma\gamma\to \gamma \nu\bar\nu$. In the second part, we present results of
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.
