Probing muonic forces with neutron star binaries

We show that gravitational wave emission from neutron star binaries can be used to discover any generic long-ranged muonic force due to the large inevitable abundance of muons inside neutron stars. As a minimal consistent example, we focus on a gauged U(1)$_{L_\mu - L_\tau}$ symmetry. In pulsar binaries, such U(1)$_{L_\mu - L_\tau}$ vectors induce an anomalously fast decay of the orbital period through the emission of dipole radiation. We study a range of different pulsar binaries, finding the most powerful constraints for vector masses below ${\cal O}(10^{-18} {\rm eV})$. For merging binaries the presence of muons in neutron stars can result in dipole radiation as well as a modification of the chirp mass during the inspiral phase. We make projections for a prospective search using both the GW170817 and S190814bv events and find that current data can discover light vectors with masses below ${\cal O}(10^{-10} {\rm eV})$. In both cases, the limits attainable with neutron stars reach gauge coupling $g^\prime\lesssim 10^{-20}$, which are many orders of magnitude stronger than previous constraints. We also show projections for next generation experiments, such as Einstein Telescope and Cosmic Explorer.