Finite Volume Corrections to the Electromagnetic Mass of Composite Particles

TL;DR

This paper investigates finite volume effects on the electromagnetic mass of composite particles in lattice QED, revealing the importance of antiparticle contributions and extending calculations to higher order for light nuclei.

Contribution

It provides a detailed analysis of antiparticle mode contributions to finite volume electromagnetic masses and extends existing calculations to higher order for composite particles.

Findings

Antiparticle modes contribute to finite-volume electromagnetic mass of composite spinors.

Finite volume effects for nucleon mass vanish, consistent with locality.

Extended calculations are relevant for light nuclei mass corrections.

Abstract

The long-range electromagnetic interaction presents a challenge for numerical computations in QCD + QED. In addition to power-law finite volume effects, the standard lattice gauge theory approach introduces non-locality through removal of photon zero-momentum modes. The resulting finite volume effects must be quantitatively understood; and, to this end, non-relativistic effective field theories are an efficient tool, especially in the case of composite particles. Recently an oddity related to non-locality of the standard lattice approach was uncovered by the Budapest-Marseille-Wuppertal collaboration. Explicit contributions from antiparticles appear to be required so that finite volume QED results for a point-like fermion can be reproduced in the effective field theory description. We provide transparency for this argument by considering point-like scalars and spinors in finite volume QED using the method of regions. For the more germane case of composite particles, we determine that antiparticle modes contribute to the finite-volume electromagnetic mass of composite spinors through terms proportional to the squares of time-like form factors evaluated at threshold. We extend existing finite volume calculations to one order higher, which is particularly relevant for the electromagnetic mass of light nuclei. Additionally, we verify that the analogous finite volume contributions to the nucleon mass in chiral perturbation theory vanish in accordance with locality.