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

We study the correction to the radiative $π^0$ 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 $<PV_μV_ν>$ in the (Euclidean) momentum space, which corresponds to the $π^0\rightarrow γ^*γ^*$ 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 $π^0\rightarrow γγ$ decay width including finite mass correction.

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