Pion Polarizabilities and Volume Effects in Lattice QCD

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.

5 figs., 19pp

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Cited by in corpus (13)

• Meson masses in electromagnetic fields with Wilson fermions
• Extracting Electric Polarizabilities from Lattice QCD
• Pion magnetic polarisability using the background field method
• The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory
• External Momentum, Volume Effects, and the Nucleon Magnetic Moment
• Volume Effects for Pion Two-Point Functions in Constant Electric and Magnetic Fields
• Exponential reduction of finite volume effects with twisted boundary conditions
• Nucleon in a periodic magnetic field: Finite-volume aspects
• Chiral extrapolation of the charged-pion magnetic polarizability with Padé approximant
• Finite volume corrections to forward Compton scattering off the nucleon
• Chiral extrapolation of the magnetic polarizability of the neutral pion
• Pion polarizabilities: Theory vs Experiment
• Charged Hadron Properties in Background Electric Fields