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 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 at fixed lattice spacing (a−1 ≃ 1.730 GeV) on a 483× 96 volume with Nf = 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 QEDL 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 |Vus|/|Vud| 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.
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 α and (m u − m d )/Λ QCD . We use QED L for the inclusion of electromagnetism, and discuss here the non-locality of this prescription which has significant impact on the infinite-volume extrapolation.
In recent years, lattice determinations of non-perturbative quantities such as f K and f π , which are relevant for V us and V ud , have reached an impressive precision of 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 α 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 QED L formulation.
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