Two-Neutrino Five-Photon Scattering at Low Energies

We extend earlier constructions of the effective action for neutrino-photon scattering, using the connection between low-energy neutrino-photon and photon-photon scattering together with the known effective Lagrangian describing low-energy photon scattering in QED. We use this effective action to calculate analytic expressions for the low-energy cross section for the (unpolarised) processes $ν\nubar \to 5 γ$, $νγ\to ν+ 4 γ$ and $γγ\to ν\nubar + 3 γ$. As a byproduct we derive compact expressions for the $N$-body phase-space integrals for massless particles, including those having non-trivial tensor-structure.