Abstract
We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.
Highlights
Precision further is mandatory in view of experimental progress [12]
We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD
In this work we present the first prediction of the form factor f+Kπ(0) with physical valence and sea quark masses in the continuum limit of domain wall lattice QCD with Nf = 2 + 1 dynamical flavours
Summary
In practice we determine the two matrix elements (2.1) and (2.2) from the time dependence of combinations of Euclidean QCD two- and three-point correlation functions which are the output of the actual simulation. The superscript B in the denominator indicates that we take the bare (unrenormalised) current in the three-point function While both ZVπ and ZVK obtained in this way renormalise the flavour-changing vector current in (2.1) we note that they differ by mass dependent cutoff effects. As is evident from eq (2.2) the vector form factor at zero momentum transfer can be extracted directly from a fit to the three point functions of the scalar current. The vector current matrix element in eq (2.1) is instead parameterised in terms of two form factors These are readily extracted from a simultaneous fit to the correlation function data for both time- and space-components of the vector current
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