ALP Production from Abelian Gauge Bosons: Beyond Hard Thermal Loops

Previous computations of feebly interacting particle production have encountered issues with unphysical (negative) interaction rates at soft momenta. We address this problem by studying the production of Axion-Like Particles (ALPs) coupled to $U(1)$-gauge fields, employing the full form of 1PI-resummed gauge boson propagators. This approach avoids the need for matching or subtraction procedures, ensuring physically consistent results. We find that the ALP production rate remains positive across all momentum scales and identify the dominant production mechanisms. At soft ALP momenta ($p \lesssim g^2 T$), interactions involving two spacelike gauge bosons dominate the production rate, surpassing other channels by an order of magnitude. In particular, using the full gauge boson propagator suggests that at even softer momenta ($p \lesssim g^4 T$), production involving two timelike gauge bosons becomes significant, potentially exceeding other contributions by another order of magnitude. Using these insights, we update the thermal ALP abundance and refine the estimate of the average ALP momentum, providing important input for structure formation constraints on ALP dark matter in the keV mass range.