Lattice phenomenology of heavy quarks using dynamical fermions
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The Standard Model of particle physics is believed to be only the low energy limit of a more fundamental theory. In order to determine its range of validity, a major part of theoretical and experimental efforts in physics is dedicated to precision tests of the Standard Model. Lattice QCD is a non-perturbative, first-principles approach to Quantum Field Theory. It plays an important role in flavor physics by providing calculations of non-perturbative strong interaction contributions to weak processes involving quarks. Measurements of hadronic quantities can be used to constrain the Standard Model as well as theories Beyond the Standard Model. The first part of this thesis contains theoretical developments regarding non-perturbative renormalization. A new renormalization scheme, RI/mSMOM, for fermion bilinear operators in QCD at non-vanishing quark mass is presented. In order to investigate the properties of the mSMOM scheme, an explicit one-loop computation in perturbation theory using dimensional regularization is performed. Numerically, vertex functions are generated on the lattice, with an appropriate projector, based on the RI/SMOM scheme and the renormalization factors are extracted. Quantities measured include renormalization of the axial current ZA, required to renormalize the axial current entering the computation of the decay constant and the renormalization of the bag parameter. The second part of this report focuses on flavor physics phenomenology on the lattice. It presents results of the first run of the RBC/UKQCD charm project with (2+1)-flavor Domain Wall fermions. Observables and matrix elements are measured on lattices with Iwasaki gauge action. There are two ensembles at the physical point with inverse lattice spacings 1.73 and 2.36 GeV and a third finer ensemble at 2.76 GeV as well as four other auxiliary ensembles with smaller volumes and heavier pion masses which are used to perform the continuum extrapolations. The quantities measured in the region of the charm quark mass are meson masses, decay constants, the matrix element of the OV V +AA operator, the neutral D-meson mixing parameter B and the SU(3) breaking ratio ξ.