Two-photon decay of $\pi^0$ from two-flavor lattice QCD

Abstract

We study the correction to the radiative $\pi^0$ decay width due to finite light quark mass. Using lattice QCD with the overlap fermion formulation, we calculate the three-point function of the form $<PV_\mu V_\nu>$ in the (Euclidean) momentum space, which corresponds to the $\pi^0\rightarrow \gamma^*\gamma^*$ amplitude. To fit the lattice data, we use two different modifications of vector meson dominance (VMD) ansatz. One is a combined form of VMD with the next-to-leading order (NLO) chiral perturbation theory (ChPT), and the other is a resummed form of pion-loop diagrams. We extract one of the low energy constants in NLO ChPT, and estimate $\pi^0\rightarrow \gamma\gamma$ decay width including finite mass correction.