The neutral pion decay and the chiral anomaly on the lattice

TL;DR

This paper presents a lattice QCD calculation of the neutral pion decay into two photons, accurately reproducing the chiral anomaly and matching experimental results with high precision.

Contribution

We introduce a lattice QCD approach using overlap fermions and all-to-all propagators to compute the c0^0d7b3d2 transition form factor and decay width, explicitly capturing the chiral anomaly.

Findings

Reproduces the ABJ anomaly in the chiral limit

Achieves agreement with experimental decay width at physical pion mass

Provides a precise lattice calculation of the c0^0d7b3d2 transition form factor

Abstract

We perform a lattice QCD calculation of the \pi^0\to\gamma\gamma transition form factor and the associated decay width. We use a Euclidean time integral of the relevant three-point function to compute the decay amplitude for two-photon final state, which is a non-QCD state. We use the all-to-all quark propagator technique to carry out this integral as well as to include the disconnected quark diagram contributions. We execute the calculation using the overlap fermion formulation, which ensures the exact chiral symmetry on the lattice and produces the chiral anomaly through the Jacobian of the chiral transformation. We examine various sources of systematic effects except for possible discretization effect. Our final results for the form factor and the decay width reproduce the ABJ anomaly in the chiral limit and agree with the experimental measurements at the physical pion mass with a precision of a few percent.