Isospin Breaking in Lattice QCD Computations of Decay Amplitudes

TL;DR

This paper discusses the development and implementation of a framework to include isospin-breaking effects, such as electromagnetic corrections, in lattice QCD calculations of decay amplitudes, enhancing the precision of Standard Model parameter determinations.

Contribution

The paper introduces a novel framework for incorporating isospin-breaking effects into lattice QCD computations of leptonic and semileptonic decay amplitudes.

Findings

Framework successfully applied to leptonic decays P→ℓν̄_ℓ(γ)

Numerical results demonstrate improved precision in decay amplitude calculations

Ongoing extension to semileptonic decays P₁→P₂ℓν̄_ℓ(γ)

Abstract

The remarkable recent progress in the precision of Lattice QCD computations for a number of physical quantities relevant for flavour physics has motivated the introduction of isospin-breaking effects, including in particular electromagnetic corrections, to the computations. The isospin breaking corrections are necessary to fully exploit this improved precision for the determination of the fundamental parameters of the Standard Model, including the CKM matrix elements, and to look for deviations from experimental measurements which might signal the presence of new physics. Together with colleagues from Rome, we have developed and implemented a framework for including isospin-breaking corrections in leptonic decays $P\to\ell\bar\nu_\ell(\gamma)$, where $P$ is a pseudoscalar meson and $\ell$ a charged lepton, and the theoretical framework and numerical results are reviewed below. The status of our studies to extend this framework to semileptonic decays $P_1\to P_2\ell\bar\nu_\ell(\gamma)$, where $P_{1,2}$ are pseudoscalar mesons, is also presented.