Prominent enhancement of axion thermalization rate from axion-kaon interactions

The axion thermalization rate is a crucial input to determine the hot dark matter bound of axions, resulting from the scattering processes in the thermal bath of early Universe. We demonstrate that the commonly employed axion thermalization rate by including the $a\pi \leftrightarrow \pi \pi$ channel alone is significantly underestimated for the temperature $T$ above 100~MeV. This is obtained through the systematical calculation of the axion-light flavor meson scattering amplitudes within the framework of the chiral unitarization approach, paying special attention to the $aK\leftrightarrow \pi K$ reaction. Hadron resonances appearing in $aK\leftrightarrow \pi K$ amplitudes significantly enlarge the cross sections, which turn out to be much bigger than that of $a\pi \leftrightarrow \pi \pi$. The axion thermalization rate is then substantially enhanced by the $aK\leftrightarrow \pi K$ channel for $T\gtrsim 100$~MeV. Especially at $T\simeq 130$~MeV, the contribution from the $aK\leftrightarrow \pi K$ reaction to the axion thermalization rate exceeds the $a\pi \leftrightarrow \pi \pi$ one. Obviously more stringent constraints on the axion parameters are obtained, when confronting the number of extra relativistic degrees of freedom $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ from Planck${}^{\mathrm{\prime }}$18.