# $\pi^0$ to two-photon decay in lattice QCD

Research paper by E. Shintani, S. Aoki, S. Hashimoto, T. Onogi, N. Yamada

Indexed on: 01 Dec '09Published on: 01 Dec '09Published in: High Energy Physics - Lattice

#### Abstract

We calculate the neutral pion ($\pi^0$) to off-shell two photon ($\gamma^*\gamma^*$) transition form factor in lattice QCD. The transition form factor can be extracted from the three-point function of the form (axial-vector)-(vector)-(vector) as a function of off-shell two-photon momentum. Since the axial-anomaly plays an important role in the $\pi^0\to\gamma\gamma$ decay process, we employ the overlap fermion, which preserves the exact chiral symmetery on the lattice. After extrapolating to the chiral and the vanishing photon momentum limit with a fit function based on vector meson dominance (VMD) model, we find that the Adler-Bell-Jackiw anomaly is correctly reproduced.