Yuxin Liu, Zhen Liu, Andrey Shkerin, Jing Shu, Yue Zhao

We investigate neutrino effects of new long-range forces arising from gauging $B-L$, $L_e-L_{μ/τ}$ or $L_μ-L_τ$ symmetries of the Standard Model. The leptonic potential generated by astronomical bodies, such as the Earth, the Sun or a neutron star, results in the Schwinger pair production of neutrinos charged under the new gauge symmetry. The oppositely charged particles accumulate in the potential well forming a degenerate Fermi gas, while equally charged particles fly away forming a steady flux of neutrinos. We find that, for the $B-L$ and $L_e-L_{μ/τ}$ forces, these effects are too weak to be observable. For the $L_μ-L_τ$ force these effects are significant in neutron stars if the gauge coupling is $g\gtrsim 10^{-18}$. The muonic force changes the element abundances of a neutron star in equilibrium and suppresses its $L_μ-L_τ$ charge. This invalidates the constraint on $g$ from neutron star mergers, at $g\gtrsim 10^{-17}$. Furthermore, for such values of $g$, the neutrino flux produced by the Schwinger effect could potentially be detected from a single young neutron star at a distance of $\simeq 100$ pc, with the typical neutrino energy $E_ν\sim 100$ MeV. A dedicated search for such a signal will reassert the bound $g\lesssim 10^{-18}$.