Near-Physical Point Lattice Calculation of Isospin-Breaking Corrections to $K_{\ell2}/\pi_{\ell2}$

TL;DR

This paper reports on a lattice QCD calculation of isospin-breaking effects in light meson leptonic decays, crucial for precise determination of CKM matrix elements, using a perturbative approach with near-physical quark masses.

Contribution

First lattice QCD study to include electromagnetic and strong isospin-breaking effects in light meson decay calculations with near-physical quark masses.

Findings

Implemented perturbative isospin-breaking corrections in lattice QCD

Used electro-quenched approximation with QED_L formulation

Achieved improved precision in meson decay constants

Abstract

In recent years, lattice determinations of non-perturbative quantities such as $f_K$ and $f_\pi$, 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 $\alpha$ 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.