Supernova axion emissivity with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1232</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> resonance in heavy baryon chiral perturbation theory
Shu-Yu Ho, Jong‐Kuk Kim, Pyungwon Ko, Jae-hyeon Park
Abstract
In this paper, we evaluate the energy loss rate of supernovae induced by the axion emission process ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+a$ with the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance in the heavy baryon chiral perturbation theory for the first time. Given the axion-nucleon-$\mathrm{\ensuremath{\Delta}}$ interactions, we include the previously ignored $\mathrm{\ensuremath{\Delta}}$-mediated graphs to the ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+a$ process. In particular, the ${\mathrm{\ensuremath{\Delta}}}^{0}$-mediated diagram can give a resonance contribution to the supernova axion emission rate when the center-of-mass energy of the pion and proton approaches the $\mathrm{\ensuremath{\Delta}}(1232)$ mass. With these new contributions, we find that for the typical supernova temperatures, compared with the earlier work with the axion-nucleon (and axion-pion-nucleon contact) interactions, the supernova axion emissivity can be enhanced by a factor of $\ensuremath{\sim}4(2)$ in the Kim-Shifman-Vainshtein-Zakharov model and up to a factor of $\ensuremath{\sim}5(2)$ in the Dine-Fischler-Srednicki-Zhitnitsky model with small $\mathrm{tan}\ensuremath{\beta}$ values. Remarkably, we notice that the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance gives a destructive contribution to the supernova axion emission rate at high supernova temperatures, which is a nontrivial result in this study.