Two-Particle Elastic Scattering in a Finite Volume Including QED

TL;DR

This paper derives finite-volume energy quantization conditions for two charged particles including QED effects, facilitating lattice QCD+QED studies of hadron interactions with long-range electromagnetic forces.

Contribution

It provides the first perturbative treatment of QED corrections to two-particle finite-volume spectra, extending Luscher's method to include electromagnetic interactions.

Findings

Derived leading QED corrections to finite-volume energy levels.

Provided approximate formulas for energy eigenvalues with QED effects.

Focused on two spinless hadrons in the A1+ representation, with potential for generalization.

Abstract

The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A1+ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.