QED_r: a finite-volume QED action with redistributed spatial zero-momentum modes

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 QEDr, 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 O(1/L3) in the commonly used QEDL 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 QEDr 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 O(1/L3) effects in leptonic decays. The removal of such contributions, shifting the leading contamination to O(1/L4), will help to reduce the systematic uncertainties associated with finite-volume effects in future lattice QCD+QED calculations.