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

Abstract

We describe a first-principles method to apply lattice QCD to compute the order ${\alpha }_{\mathrm{EM}}$ corrections to $K\to \pi \ell {\nu }_{\ell }$ 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.

Comments: 9 pages, 1 figure, presented at the 40th International Symposium on Lattice Field Theory, (LATTICE2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA