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 meff²=kαkα m eff 2 = k α k α . This makes the otherwise forbidden decay γ → ν ν ̄ γ → ν ν ¯ kinematically allowed. The process proceeds through the Standard Model one-loop neutrino electromagnetic vertex and is therefore strongly suppressed. Using the low- q² 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, γ → e⁺e⁻ γ → 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.