Neutrino astronomy as a probe of physics beyond the Standard Model: decay of sub-MeV $B$-$L$ gauge boson dark matter

The $U(1)_{B\textrm{--}L}$ symmetry, the essential component in the seesaw mechanism and leptogenesis, is naturally equipped with a massive gauge boson. If this gauge boson is the dark matter, the scenario consistent with the seesaw mechanism predicts the gauge coupling to be of the order of $\mathcal{O}(10^{-19})$ for masses $\lesssim1$ MeV, dominantly decaying into active neutrinos. We stress and explore the important role of astrophysical neutrinos of energies from $\mathcal{O}(1)$ keV to $\sim1$ MeV in testing the well-motivated $B$-$L$ symmetry extension to the Standard Model, which has been missed in the literature to date. Compared to other dark matter models, the neutrino flux in the sub-MeV energy range is a unique prediction in our setup and, once detected, would serve as a smoking gun for the existence of this $B$-$L$ gauge boson and its role as the dark matter particle, opening new windows to tackle cosmological and astrophysical conundra.