Abstract
The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the and leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with dynamical quarks. The relative leading-order e.m. and strong isospin-breaking corrections to the decay rates are 1.53(19)% for decays and 0.24(10)% for decays. Using the experimental values of the and decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element , reducing by a factor of about 1.8 the corresponding uncertainty in the particle data group review. Our calculation of allows also an accurate determination of the first-row Cabibbo-Kobayashi-Maskawa unitarity relation . Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full theory and an improved renormalization procedure in which the bare lattice operators are renormalized nonperturbatively into the regularization independent momentum subtraction (RI’-MOM) scheme and subsequently matched perturbatively at into the W-regularization scheme appropriate for these calculations.
3 More- Received 28 April 2019
DOI:https://doi.org/10.1103/PhysRevD.100.034514
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Published by the American Physical Society