Constraints from the duration of supernova neutrino burst on on-shell light gauge boson production by neutrinos

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In this article, we study the on-shell production of low-mass vector mediators from neutrino-antineutrino coalescence in the core of proto-neutron stars.

• Taking into account the radial dependence of the density, energy, and temperature inside the proto-neutron star, we compute the neutrino-antineutrino interaction rate in the star interior in the well-motivated $U(1)_{L_{\mu}-L_{\tau}}$ model.
• First, we determine the values of the coupling above which neutrino-antineutrino interactions dominate over the Standard Model neutrino-nucleon scattering.
• We argue that, although in this regime a redistribution of the neutrino energies might take place, making low-energy neutrinos more trapped, this only affects a small part of the neutrino population and it cannot be constrained with the SN 1987A data.