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.
The decays and mixing of K mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant G F and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities.
The rare Hyperon decay Σ + → ℓ + ℓ − is an → flavour changing neutral current, and is therefore suppressed in within the Standard Model, making it an excellent probe for new physics. The process is dominated by long distance processes and therefore lattice QCD is the only existing technique to obtain a first principles Standard Model theoretical prediction. We present our work on an unphysical exploratory study of the rare Hyperon decay on the lattice, including an investigation into the applicability of source-sink sampling for this decay, and we show a generalisation of the summed method for arbitrary 3-point functions and 4-point functions. In addition we show preliminary results for a computation of the → semileptonic Hyperon decays.
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