Axion emission from supernova with axion-pion-nucleon contact interaction

We examine the axion emission from supernovae with a complete set of relevant axion couplings including the axion-pion-nucleon contact interaction which was ignored in the previous studies. Two processes are affected by the axion-pion-nucleon contact interaction, $\pi^-+p \rightarrow n + a$ and $n+p\rightarrow n+p+a$, and these processes can be the dominant source of axions for some region in the axion parameter space or in astrophysical conditions encountered inside supernovae. We find that the contact interaction can enhance the axion emissivity of $\pi^-+p \rightarrow n + a$ by a factor of $2-4$, while the effect on $n+p\rightarrow n+p+a$ is not significant. We also discuss the relative importance of other pion-induced processes such as $\pi^0+n\rightarrow n+a$ and $\pi^-+\pi^0\rightarrow \pi^-+a$.