Pion Polarizabilities and Volume Effects in Lattice QCD

TL;DR

This paper uses chiral perturbation theory to analyze how finite volume effects influence the extraction of pion electromagnetic polarizabilities from lattice QCD, highlighting limitations of current methods due to volume and zero-mode complications.

Contribution

It derives finite volume corrections for pion Compton scattering and discusses the challenges in relating these to polarizability measurements in lattice QCD.

Findings

Finite volume effects on Compton tensor are quantified.

Volume effects cannot be directly inferred from form factors.

Momentum expansion limitations prevent volume correction estimates.

Abstract

We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched QCD, and quenched QCD simulations. On a torus, volume dependence of electromagnetic observables is complicated by SO(4) breaking, as well as photon zero-mode interactions. We determine finite volume corrections to the Compton scattering tensor of pions. We argue, however, that such results cannot be used to ascertain volume corrections to polarizabilities determined in lattice QCD with background field methods. Connection is lacking because momentum expansions are not permitted in finite volume. Our argument also applies to form factors. Volume effects for electromagnetic moments cannot be deduced from finite volume form factors.