Lattice QCD and the two-photon decay of the neutral pion

TL;DR

This paper explores the theoretical calculation of the neutral pion's two-photon decay amplitude using lattice QCD, highlighting how finite-volume effects influence the results and providing a new derivation approach.

Contribution

It rederives the decay amplitude expression in terms of Euclidean correlation functions, clarifying finite-volume effects for timelike photons in lattice QCD.

Findings

Decay amplitude approaches infinite-volume value exponentially with box size.

Provides a new derivation of decay amplitude in Euclidean space.

Clarifies finite-volume effects for timelike photon processes.

Abstract

Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wavefunction at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.