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Article
Report number	arXiv:2211.12865 ; CERN-TH-2022-193 ; LU-TP 22-59
Title	Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses
Author(s)	Boyle, Peter (Brookhaven ; Edinburgh U.) ; Di Carlo, Matteo (Edinburgh U.) ; Erben, Felix (Edinburgh U.) ; Gülpers, Vera (Edinburgh U.) ; Hansen, Maxwell T. (Edinburgh U.) ; Harris, Tim (Edinburgh U.) ; Hermansson-Truedsson, Nils (Bern U. ; Lund U., Dept. Theor. Phys.) ; Hodgson, Raoul (Edinburgh U.) ; Jüttner, Andreas (Southampton U. ; CERN) ; hÓgáin, Fionn Ó. (Edinburgh U.) ; Portelli, Antonin (Edinburgh U.) ; Richings, James (Edinburgh U. ; Southampton U. ; Edinburgh U., EPCC) ; Yong, Andrew Zhen Ning (Edinburgh U.)
Publication	2023-02-27
Imprint	2022-11-23
Number of pages	66
Note	66 pages, 23 figures and 4 tables
In:	JHEP 2302 (2023) 242
DOI	10.1007/JHEP02(2023)242
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-lat ; Particle Physics - Lattice
Abstract	The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than $\mathrm{O}(1\%)$, require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed with $N_\mathrm{f}=2+1$ dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the $\mathrm{QED_L}$ prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on $|V_\mathrm{us}|/|V_\mathrm{ud}|$ and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2023-2025 The Authors (License: CC-BY-4.0), sponsored by SCOAP³

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