# Nucleon in a periodic magnetic field: Finite-volume aspects

## TL;DR

This paper refines methods for extracting nucleon scattering amplitudes using lattice QCD in periodic magnetic fields, addressing finite-volume effects and establishing conditions for perturbative analysis.

## Contribution

It extends previous work by refining the background field technique, analyzing zero frequency limits, and setting a framework for finite-volume correction evaluation.

## Key findings

- Reproduces known zero frequency limit results.
- Establishes an upper bound for external field magnitude.
- Provides a framework for finite-volume correction analysis.

## Abstract

The paper presents an extension and a refinement of our previous work on the extraction of the doubly virtual forward Compton scattering amplitude on the lattice by using the background field technique, Phys. Rev. D 95, 031502 (2017) (arXiv:1610.05545). The zero frequency limit for the periodic background field is discussed, in which the well-known result is reproduced. Further, an upper limit for the magnitude of the external field is established for which the perturbative treatment is still possible. Finally, the framework is set for the evaluation of the finite-volume corrections allowing for the analysis of upcoming lattice results.