Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at O(α) 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/L2) [compared to the O(1/L3) 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).PRVDAQ1550-799810.1103/PhysRevD.91.074506] for using lattice simulations to compute the decay widths at O(α), with the remaining finite-volume effects starting at order O(1/L2). 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.