Structure-dependent electromagnetic finite-volume effects through order $1\mathrm{/}{L}^3$

We consider electromagnetic finite-volume effects through order $1\mathrm{/}{L}^3$ 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${}_{\text{L}}$ 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${}_{\text{C}}$, QED${}_{\text{L}}$ and QED${}_{\text{L}}^{\text{IR}}$, the latter being a class of non-local formulations generalising QED${}_{\text{L}}$. One choice within this class is QED${}_{\text{r}}$, first introduced at this conference, and we show that the effects of non-locality for the $1\mathrm{/}{L}^3$ term in the expansion can be removed. We observe that there are still $1\mathrm{/}{L}^3$ contributions unrelated to the (non-)locality of the studied QED formulations, but rather to collinear singularities in the physical amplitudes.