We present a new calculation of the K → π semileptonic form factor at zero momentum transfer in domain wall lattice QCD with N f = 2+1 dynamical quark flavours. By using partially twisted boundary conditions we simulate directly at the phenomenologically relevant point of zero momentum transfer. We perform a joint analysis for all available ensembles which include three different lattice spacings (a = 0.09 -0.14 fm), large physical volumes (m π L > 3.9) and pion masses as low as 171 MeV. The comprehensive set of simulation points allows for a detailed study of systematic effects leading to the prediction f Kπ + (0) = 0.9670(20)( +18 −46 ), where the first error is statistical and the second error systematic. The result allows us to extract the CKM-matrix element |V us | = 0.2237( +13 − 8 ) and confirm first-row CKM-unitarity in the Standard Model at the sub per mille level.

Abstract:We discuss all-to-all quark propagator techniques in two (related) contexts within Lattice QCD: the computation of closed quark propagators, and applications to the so-called "eye diagrams" appearing in the computation of non-leptonic kaon decay amplitudes. Combinations of low-mode averaging and diluted stochastic volume sources that yield optimal signal-to-noise ratios for the latter problem are developed. We also apply a recently proposed probing algorithm to compute directly the diagonal of the inverse Dirac operator, and compare its performance with that of stochastic methods. At fixed computational cost the two procedures yield comparable signal-to-noise ratios, but probing has practical advantages which make it a promising tool for a wide range of applications in Lattice

We present an update on the RBC/UKQCD collaboration's results for the K → π semileptonic vector form factor at zero momentum transfer from simulations of chiral fermions. Our results cover the whole range of light quark masses between the SU(3)-symmetric and the physical point for three lattice spacings and large physical volumes. Using partially twisted boundary conditions we calculate the form factor directly at zero momentum transfer. The comprehensive set of data points allows for turning the extrapolation in the quark mass into an interpolation around the physical point thereby removing the dominant systematic uncertainty in previous results, the chiral extrapolation. We briefly discuss our prediction in view of Standard Model phenomenology.

The CKM matrix element |V us | can be extracted from the experimental measurement of semileptonic K → π decays. The determination depends on theory input for the corresponding vector form factor in QCD. We present a preliminary update on our efforts to compute it in N f = 2 + 1 lattice QCD using domain wall fermions for several lattice spacings and with a lightest pion mass of about 170 MeV. By using partially twisted boundary conditions we avoid systematic errors associated with an interpolation of the form factor in momentum-transfer, while simulated pion masses near the physical point reduce the systematic error due to the chiral extrapolation.

We present an algorithm to automatically derive Feynman rules for lattice perturbation theory in background field gauge. Vertices with an arbitrary number of both background and quantum legs can be derived automatically from both gluonic and fermionic actions. The algorithm is a generalisation of our earlier algorithm based on prior work by Lüscher and Weisz. We also present techniques allowing for the parallelisation of the evaluation of the often rather complex lattice Feynman rules that should allow for efficient implementation on GPUs, but also give a significant speed-up when calculating the derivatives of Feynman diagrams with respect to external momenta.