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

Abstract

We calculate the neutral pion (${\pi }^0$) to off-shell two photon (${\gamma }^{\ast }{\gamma }^{\ast }$) 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.

Comments: 7 pages. Talk presented at The XXVII International Symposium on Lattice Field Theory, July 26-31 2009, Peking University, Beijing, China