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

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.