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 ^sub +^^sup K^ ^sup pi^(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 arrow right pi decays for a determination of the CKM-matrix element for which we predict |V ^sub us^| = 0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.
Hadronic matrix elements evaluated on the lattice can be converted to a continuum scheme such as \(\MSbar\) using intermediate non-perturbative renormalisation schemes. Discretisation effects on the ...lattice and convergence of the continuum perturbation theory are both scheme dependent and we explore this dependence in the framework of the Rome-Southampton method for generalised kinematics. In particular, we implement several non-exceptional {\em interpolating} momentum schemes, where the momentum transfer is {\em not} restricted to the symmetric point defined in RI/SMOM. Using flavour non-singlet quark bilinears, we compute the renormalisation factors of the quark mass and wave function for \(N_f=3\) flavours of dynamical quarks. We investigate the perturbative and non-perturbative scale-dependencies. Our numerical results are obtained from lattice simulations performed with Domain-Wall fermions, based on ensembles generated by RBC-UKQCD collaborations; we use two different lattice spacings \(1/a \sim 1.79 \) and \(2.38\) GeV. We also give the numerical values for the relevant anomalous dimensions and matching coefficients at next-to-next-to-leading order.
We compute the renormalisation factors of the quark mass and wave function using IMOM (Interpolating MOMenta) schemes. The framework is the Rome-Southampton non-renormalisation method, but the ...momentum transfer in the quark bilinears is not restricted to zero or to the symmetric point. We study the scale dependence, infrared contamination and lattice artefacts for different values of this momentum transfer and for two different kinds of projectors. For the numerical simulations, we use data generated by the RBC-UKQCD collaborations, with \(N_f = 2+1\) flavours of Domain-Wall fermions, and inverse lattice spacing of \(1.79 \) and \(2.38\) GeV.
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