Nucleon-nucleon bremsstrahlung of dark gauge bosons and revised supernova constraints

We calculate the rate of production of hypothetical light vector bosons (LVBs) from nucleon-nucleon bremsstrahlung reactions in the soft radiation limit directly in terms of the measured nucleon-nucleon elastic cross sections. We use these results and the observation of neutrinos from supernova SN1987a to deduce constraints on the couplings of vector bosons with masses $\lesssim 200$ MeV to either electric charge (dark photons) or to baryon number. We establish for the first time strong constraints on LVB that couple only to baryon number, and revise earlier constraints on the dark photon. For the latter, we find that the excluded region of parameter space is diminished by about a factor of 10.