Near-Physical Point Lattice Calculation of Isospin-Breaking Corrections to $K_{\ell 2}/\ddot{I}{€}_{\ell 2}$

Abstract

In recent years, lattice determinations of non-perturbative quantities such as $f_K$ and $f_{\ddot{I}}€$, which are relevant for $V_{us}$ and $V_{ud}$, have reached an impressive precision of $\mathcal{O}(1\%)$ or better. To make further progress, electromagnetic and strong isospin breaking effects must be included in lattice QCD simulations. We present the status of the RBC/UKQCD lattice calculation of isospin-breaking corrections to light meson leptonic decays. This computation is performed in a (2+1)-flavor QCD simulation using Domain Wall Fermions with near-physical quark masses. The isospin-breaking effects are implemented via a perturbative expansion of the action in $\hat{I}\pm$ and $(m_u-m_d)$. In this calculation, we work in the electro-quenched approximation and the photons are implemented in the Feynman gauge and ${\text{QED}}_{\text{L}}$ formulation.

11 pages, 4 figures; Updated Author(s) metadata