Axions, SN 1987 A, and one-pion exchange

The axion mass constraint which follows from SN 1987A, the exclusion of axion masses between ${10}^{-3\mathrm{}}$ eV and 2 eV, is the most stringent astrophysical bound, and such has received much scrutiny. Nucleon-nucleon, axion bremsstrahlung is the primary mechanism for axion emission from the nascent neutron star associated with SN 1987A, and the rate for this process has been calculated in the one-pion-exchange (OPE) approximation. It has been suggested that by using OPE to calculate the cross section for the analogue process, $\mathrm{pp}\to pp+{\pi }^0$, and comparing the result to experimental data one can test the validity of this approximation. We have carefully evaluated the cross section for $\mathrm{pp}\to pp+{\pi }^0$ using OPE and find excellent agreement (to better than a factor of 2) with the experimental data. Within the context of the nonlinear sigma model we also address the effects of finite density on axion emission, and conclude that these effects are likely to change the axion emission rate by at most a factor of a few (and could even enhance the axion emission rate). Thus we conclude that the axion emission rate based upon OPE is reliable to at least a factor of a few, thereby validating the very stringent limits to the axion mass based upon SN 1987A.