Kaon semileptonic form factor with near physical domain wall quarks
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The CKM matrix element |Vus| can be extracted from the experimental measurement of semileptonic K → π decays and theoretical input for the corresponding vector form factor in QCD. The thesis performs a major improvement of the RBC/UKQCD programme to calculate Kl3 form factor in Nf = 2+1 Lattice QCD using domain wall fermions. We use data from several lattice spacings and dfferent quark masses with lightest pion mass of about 170MeV. Systematic error corresponding to interpolation in the momentum transfer is avoided using partially twisted boundary conditions. Using simulated quark masses near the physical point, reduce the systematic error due to the mass extrapolation. This work explores different kinematic arrangements of pion and Kaon momenta for twisted boundary conditions. This thesis proposes a new ansatz for mass extrapolation. Analysing three sets of simulation data allows for a detailed study of systematic effects leading to the prediction f+kπ (0) = 0:9671(17)(+18-46), where the first error is statistical and the second error systematic. The result allows us to extract the CKM matrix element |Vus| = 0:2237(+13-8) and confirm unitarity of the first row CKM matrix in the Standard Model. Also in this thesis, we discuss porting of Clover Lattice fermion action to Blue Gene-Q architecture. Clover action achieves maximum efficiency of 29.1% for single precision with good weak scaling. Strong scaling shows local volume dependency. In a study of different iterative solvers for Domain Wall Fermion action (DWF), we find that Modified Conjugate Residual(MCR) and Multishift MCR as the most efficient solver compared to CG and GCR. A new probing technique for estimating the diagonal of the inverse Dirac operator in Lattice QCD is introduced and this method is found to be closer to the exact solution than stochastic methods.