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We demonstrate that the leading and next-to-leading finite-volume effects inthe 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 isanalogous to a similar result for the spectrum but with some fundamentaldifferences, most notably the presence of infrared divergences in decayamplitudes. 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 thespectrum). We calculate the universal finite-volume effects, which requires anextension of previously developed techniques to include a dependence on anexternal three-momentum (in our case, the momentum of the final state lepton).The result can be included in the strategy proposed inRef.\,\cite{Carrasco:2015xwa} for using lattice simulations to compute thedecay widths at $O(\alpha)$, with the remaining finite-volume effects startingat order $O(1/L^2)$. The methods developed in this paper can be generalised toother decay processes, most notably to semileptonic decays, and hence open thepossibility of a new era in precision flavour physics.

Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD