Lorentz-Violating Photon Decay into Neutrinos and Constraints from PeV Photon Stability

We study the vacuum decay of a Lorentz-violating photon into a neutrino-antineutrino pair. Lorentz-violating corrections to the photon dispersion relation are parametrized through an effective invariant mass $m_{\mathrm{eff}}^{2}=k_{\alpha}k^{\alpha}$. This makes the otherwise forbidden decay $\gamma\to\nu\bar{\nu}$ kinematically allowed. The process proceeds through the Standard Model one-loop neutrino electromagnetic vertex and is therefore strongly suppressed. Using the low-$q^{2}$ anapole form factor, we derive the decay rate and apply it to TeV and PeV photons. We find that below the electron-positron threshold the neutrino channel is open but generally too slow to provide stronger constraints than existing bounds. Above the threshold, $\gamma\to e^{+}e^{-}$ dominates unless the relative photon-electron LIV parameter closes this channel. In that case, the neutrino decay gives an independent constraint on photon-neutrino relative LIV parameters.