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 hot and dense matter. We use the soft-radiation approximation and express the rates directly in terms of the measured nucleon-nucleon elastic differential cross sections. These results are combined with the observation of neutrinos from supernova SN1987a to deduce constraints on the couplings of vector bosons with masses less than or similar to 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.