Finite-Volume Corrections to Electromagnetic Masses for Larger-Than-Physical Electric Charges

Abstract

The numerical value of the fine-structure constant generally leads to small isospin-breaking effects due to electromagnetism in QCD. This smallness complicates determining isospin breaking from lattice QCD computations that include electromagnetism. One solution to this problem consists of performing computations using larger-than-physical values of the electric charge, and subsequently extrapolating (or interpolating) to the physical value of the fine-structure constant. Motivated by recent lattice QCD + QED computations of electromagnetic masses employing this setup, we consider finite-volume effects arising from the use of larger-than-physical electric charges. A modified power-counting scheme, which is based on treating the fine-structure constant as larger than its physical value, is explored. Results for perturbative QED corrections, however, are surprising. Within the framework of non-relativistic QED, multi-loop diagrams exhibit a momentum factorization property that produces exact cancellations. We determine that power-law finite-volume effects vanish at the leading two- and three-loop order, as well as the next-to-leading two-loop order. For larger-than-physical charges, we consequently expect no appreciable volume corrections beyond leading-order QED.