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 $τ/m\sim 500 Mpc/cE_ν\sim 500$ s/eV. We study the rapid decay channel $ν_i\toν_j+ϕ$, where $ϕ$ is a massless or very light scalar (possibly a Goldstone boson), and point out that one can test the coupling strength of $g_{ij}ν_iν_j$ down to $g_{ij}\lsim 10^{-8} eV/m$ by measuring the relative fluxes of $ν_{e}$, $ν_μ$ and $ν_τ$. 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.

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