Structure-dependent electromagnetic finite-volume effects through order $1/L^3$

TL;DR

This paper analyzes electromagnetic finite-volume effects up to order 1/L^3 in various QED formulations, addressing structure-dependent issues and demonstrating how certain non-local effects can be mitigated, with implications for lattice calculations.

Contribution

It introduces a general framework for volume expansions in different QED formulations and shows how to remove non-locality effects at order 1/L^3, clarifying the origin of residual contributions.

Findings

Non-locality effects at 1/L^3 can be eliminated in QED_r.

Structure-dependent effects are linked to form factors and correlation functions.

Residual 1/L^3 effects are due to collinear singularities, not non-locality.

Abstract

We consider electromagnetic finite-volume effects through order $1/L^3$ in different formulations of QED, where $L$ is the periodicity of the spatial volume. An inherent problem at this order is the appearance of structure-dependent quantities related to form factors and the analytical structure of the correlation functions. The non-local constraint of the widely used QED$_{\textrm{L}}$ regularization gives rise to structure-dependent effects that are difficult to evaluate analytically and can act as a precision bottleneck in lattice calculations. For this reason, we consider general volume expansions relevant for the mass spectrum as well as leptonic decay rates in QED$_{\textrm{C}}$, QED$_{\textrm{L}}$ and QED$_{\textrm{L}}^{\textrm{IR}}$, the latter being a class of non-local formulations generalising QED$_{\textrm{L}}$. One choice within this class is QED$_{\textrm{r}}$, first introduced at this conference, and we show that the effects of non-locality for the $1/L^3$ term in the expansion can be removed. We observe that there are still $1/L^3$ contributions unrelated to the (non-)locality of the studied QED formulations, but rather to collinear singularities in the physical amplitudes.