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arXiv · 2310.13358

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

Matteo Di Carlo·Maxwell T. Hansen·Nils Hermansson-Truedsson·Antonin Portelli
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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.

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Matteo Di Carlo, Maxwell T. Hansen, Nils Hermansson-Truedsson, Antonin Portelli. 2023-10-20. Structure-dependent electromagnetic finite-volume effects through order $1/L^3$. https://arxiv.org/abs/2310.13358

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