We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ 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 non-universal, structure-dependent terms are of O(1/L^2) (compared to the O(1/L^3) leading non-universal 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.\,\citeCarrasco:2015xwa for using lattice simulations to compute the decay widths at $O(\alpha)$, with the remaining finite-volume effects starting at order O(1/L^2). The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
Lubicz, V., Martinelli, G., Sachrajda, C., Sanfilippo, F., Simula, S., & Tantalo, N. (2017). Finite-volume QED corrections to decay amplitudes in lattice QCD. PHYSICAL REVIEW D, 95(3) [10.1103/PhysRevD.95.034504].