First lattice calculation of the QED corrections to leptonic decay rates

TL;DR

This paper presents the first lattice QED calculation of electromagnetic corrections to leptonic decay rates, providing precise results that improve upon previous theoretical estimates and account for systematic uncertainties.

Contribution

It introduces a novel lattice method to compute QED corrections to decay rates, including systematic effects and quenched QED approximation impacts.

Findings

QED correction to $K_{\mu 2}/\pi_{\mu 2}$ decay ratio is -1.22%

Results agree with Chiral Perturbation Theory estimates within uncertainties

Systematic effects and quenched QED approximation impacts are quantified.

Abstract

The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of $K_{\mu 2}$ and $\pi_{\mu 2}$ decay rates are evaluated for the first time on the lattice, following a method recently proposed. The lattice results are obtained using the gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. Systematics effects are evaluated and the impact of the quenched QED approximation is estimated. Our result for the correction to the tree-level $K_{\mu 2} / \pi_{\mu 2}$ decay ratio is $-1.22\,(16) \%$ to be compared to the estimate $-1.12\,(21) \%$ based on Chiral Perturbation Theory and adopted by the Particle Data Group.