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.
Categories: hep-lat hep-ph