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arXiv · 2501.07936

$\text{QED}_\text{r}$: a finite-volume QED action with redistributed spatial zero-momentum modes

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

We present a finite-volume QED action designed to improve the infinite-volume extrapolation of hadronic observables in precision lattice QCD+QED calculations. The action proposed in this work, which we call $\text{QED}_\text{r}$, can be seen as a particular case of the infrared-improved QED actions introduced by Davoudi et al. in 2019, and is specifically designed to remove kinematics-independent finite-volume corrections that appear at $\mathrm{O}(1/L^3)$ in the commonly used $\text{QED}_\text{L}$ formulation, where $L$ is the spatial extent of the physical volume. For a number of key observables, these effects depend on the internal structure of the hadrons and are difficult to evaluate non-perturbatively, making an analytical subtraction of the finite-volume effects impractical. We explicitly study the $\text{QED}_\text{r}$ electromagnetic finite-size effects on hadron masses and leptonic decay rates, relevant for Standard Model precision tests using the Cabibbo-Kobayashi-Maskawa matrix elements. In addition, we propose methods to remove the kinematics-dependent $\mathrm{O}(1/L^3)$ effects in leptonic decays. The removal of such contributions, shifting the leading contamination to $\mathrm{O}(1/L^4)$, will help to reduce the systematic uncertainties associated with finite-volume effects in future lattice QCD+QED calculations.

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Matteo Di Carlo, Maxwell T. Hansen, Nils Hermansson-Truedsson, Antonin Portelli. 2025-01-14. $\text{QED}_\text{r}$: a finite-volume QED action with redistributed spatial zero-momentum modes. https://arxiv.org/abs/2501.07936

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