Axion-like particle production from kaon decays within U(3) chiral theory
Kaon decays provide important constraints on the axion-like particle (ALP), particularly through the $K\toπa$ processes. In this work, we compute the $K\toπa$ decay amplitudes, as well as the $K\toππ$ decay amplitudes, at leading order within U(3) chiral perturbation theory. The $ππ$ final-state interaction effects in both processes are implemented by employing the chiral unitarization approach. The relevant weak low-energy constants are determined by fitting to the experimental data on $K\toππ$ decays. Our numerical analysis shows that the explicit $η_0$ contribution to the $K\toπa$ amplitudes is small, whereas the new weak operator unique to the U(3) theory can give a sizable contribution. The $ππ$ final-state interactions are found to be insignificant in the $K^\pm\toπ^\pm a$ decays, but give pronounced effects in the $K^0/\bar{K}^0\toπ^0a$ channels. Constraints on the ALP couplings are derived from the most recent NA62 upper limit on the $K^+\toπ^+ +invisible$ decay. For completeness, we also include constraints from the KOTO search for $K_L\toπ^0+ invisible$, the NA62 measurement of $K^+\toπ^+γγ$, and the NA48 measurement of $K_S\toπ^0γγ$.