Production of Leptophilic Bosons in Ultradegenerate Relativistic Matter

Neutron stars (NSs) are powerful factories for new particles with masses up to the 100 keV range. These compact stars contain significant populations of charged particles, notably protons, electrons and muons. We calculate the emission rates for new scalar, vector, and pseudoscalar bosons that predominantly couple to electrons and muons. For vector bosons, the in-medium renormalization of the effective couplings strongly modifies the emission rates, e.g., purely muon-philic vectors are predominantly emitted by ultra-relativistic electrons. We focus on bremsstrahlung in electromagnetic lepton-lepton or lepton-proton collisions in the ultradegenerate limit. When protons are superconducting, the scalar and vector energy loss rates scale as $T^4$, the pseudoscalar one as $T^6$, to be compared with $T^8$ for neutrino losses by the modified Urca process. For normal-conducting protons, the screening of transverse photons implies instead scalings with a power reduced by $1/3$ and thus $T^{11/3}$ for scalars and vectors, and $T^{17/3}$ for pseudoscalars. As the NS cools, such new particle losses would become important at late times, when surface photon emission begins to take over, which itself scales roughly as $T^2$ in terms of the internal temperature. Our results can be used to constrain the leptophilic coupling strengths through observed NS cooling ages.