Isospin-breaking corrections to light leptonic decays in lattice QCD+QED at the physical point

TL;DR

This paper presents a lattice QCD+QED calculation of isospin-breaking effects on light meson leptonic decays at the physical point, crucial for precision tests of the CKM matrix unitarity.

Contribution

It introduces a first-principles lattice computation of isospin-breaking corrections including electromagnetic effects with a novel treatment of finite-volume issues.

Findings

Quantified isospin-breaking corrections to meson decay rates.

Assessed the impact of QED$_L$ non-locality on infinite-volume extrapolation.

Provided data relevant for CKM matrix unitarity tests.

Abstract

We report on the physical-point RBC/UKQCD calculation of the leading isospin-breaking corrections to light-meson leptonic decays. This is highly relevant for future precision tests in the flavour physics sector, in particular the first-row unitarity of the Cabibbo-Kobayashi-Maskawa matrix containing the elements $V_{us}$ and $V_{ud}$. The simulations were performed using Domain-Wall fermions for $2+1$ flavours, and with isospin-breaking effects included perturbatively in the path integral through order $\alpha$ and $(m_u - m_d)/\Lambda _{\mathrm{QCD}}$. We use QED$_{\mathrm{L}}$ for the inclusion of electromagnetism, and discuss here the non-locality of this prescription which has significant impact on the infinite-volume extrapolation.