Radiative corrections to leptonic decays using infinite-volume reconstruction

Lattice QCD calculations of leptonic decay constants have now reached subpercent precision so that isospin-breaking corrections, including QED effects, must be included to fully exploit this precision in determining fundamental quantities, in particular the elements of the Cabibbo-Kobayashi-Maskawa matrix, from experimental measurements. A number of collaborations have performed, or are performing, such computations. In this paper we develop a new theoretical framework, based on infinite-volume reconstruction (IVR), for the computation of electromagnetic corrections to leptonic decay widths. In this method, the hadronic correlation functions are first processed theoretically in infinite volume, in such a way that the required matrix elements can be determined nonperturbatively from lattice QCD computations with finite-volume uncertainties which are exponentially small in the volume. The cancellation of infrared divergences in this framework is performed fully analytically. We also outline how this IVR treatment can be extended to determine the QED effects in semileptonic kaon decays with a similar degree of accuracy.

Automated summary

Lattice QCD calculations have achieved subpercent precision and isospin-breaking corrections, including QED effects, must be considered for accurate determination of fundamental quantities from experimental measurements. This paper presents a new theoretical framework, based on infinite-volume reconstruction (IVR), for calculating electromagnetic corrections to leptonic decay widths. The IVR method allows for nonperturbative determination of required matrix elements from lattice QCD computations with exponentially small finite-volume uncertainties. The framework also demonstrates potential for determining QED effects in semileptonic kaon decays.