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 $<P{V}_{\mu }{V}_{\nu }>$ in the (Euclidean) momentum space, which corresponds to the ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$ 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 ${\pi }^0\to \gamma \gamma$ decay width including finite mass correction.

Comments: A contribution to the XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy