Finite-volume QED corrections to decay amplitudes in lattice QCD

Abstract

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\ensuremath{\alpha})$ are universal; i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading nonuniversal, structure-dependent terms are of $O(1/{L}^{2})$ [compared to the $O(1/{L}^{3})$ leading nonuniversal corrections in the spectrum]. We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final-state lepton). The result can be included in the strategy proposed in Ref. [N. Carrasco et al.,Phys. Rev. D 91, 074506 (2015).] for using lattice simulations to compute the decay widths at $O(\ensuremath{\alpha})$, with the remaining finite-volume effects starting at order $O(1/{L}^{2})$. The methods developed in this paper can be generalized to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavor physics.