Testing neutrino instability with active galactic nuclei

Active galactic nuclei and gamma ray bursts at cosmological distances are sources of high-energy electron and muon neutrinos and provide a unique test bench for neutrino instability. The typical lifetime-to-mass ratio one can reach there is τ/m∼500 Mpc/cEν∼500 s/eV. We study the rapid decay channel νi→νj+φ, where φ is a massless or very light scalar (possibly a Goldstone boson), and point out that one can test the coupling strength of gijνiνjφ down to gij≲10−8 eV/m by measuring the relative fluxes of νe, νμ and ντ. This is orders of magnitude more stringent bound than what one can obtain in other phenomena, e.g. in neutrinoless double beta decay with scalar emission.