Volume Effects for Pion Two-Point Functions in Constant Electric and Magnetic Fields

TL;DR

This paper analyzes finite volume effects on pion two-point functions in lattice QCD under constant electric and magnetic fields, highlighting significant volume corrections to polarizabilities and the renormalization of effective action terms.

Contribution

It provides a detailed calculation of finite volume corrections for pion two-point functions in background fields using chiral perturbation theory, including polarizability shifts and renormalization insights.

Findings

Finite volume shifts to pion electric and magnetic polarizabilities are significant.

All terms in the single-particle effective action can be renormalized by infrared effects.

Gauge invariance on a torus influences the renormalization of couplings.

Abstract

We compute finite volume effects relevant for lattice QCD simulations using background fields. Focusing on constant electric and magnetic fields on a periodic lattice, we determine volume corrections to pion two-point functions using chiral perturbation theory. Among such corrections are the finite volume shifts to the electric and magnetic polarizabilities, which are numerically shown to be non-negligible. We additionally find that all terms in the single-particle effective action can be renormalized by infrared effects. This includes Born couplings to the pion current and total charge-squared, which can be renormalized due to the nature of gauge invariance on a torus.