New axion contribution to the two-photon decays of neutral pions

The presence of axions introduces new diagrams at one-loop order to the two-photon decays of the neutral pion through axion-pion mixing. In this work, we calculate this correction, missing in all current calculations, in the framework of SU(2) chiral perturbation theory. We show that the correction is proportional to the axion-photon coupling and the square of axion mass, which in turn is strongly suppressed by the axion decay constant for the classical space window but may not be negligible for the QCD axion in the MeV or even larger mass range. On the other hand, in combination with the experimental measurement of the decay width of ${\pi }^0\to \gamma \gamma$ process, this result rules out the standard QCD axion as an explanation for the possible discrepancy between the chiral perturbation theory prediction and the experimental data.