Lattice calculation of electromagnetic corrections to $K\mathrm{\ell }3$ decay

We describe a first-principles method to apply lattice QCD to compute the order ${\alpha }_{\mathrm{E}\mathrm{M}}$ corrections to $K\to \pi \mathrm{\ell }{\nu }_{\mathrm{\ell }}$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: arXiv:2304.08026.