Non-perturbative construction of heavy quark effective theory on the lattice

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The purpose of this research project is a construction of the heavy quark effective theory on the lattice, which is necessary for the simulations of heavy quark in the lattice QCD. Using such formulation, one can reduce the systematic uncertainty in the lattice calculations of various B meson matrix elements, such as the B meson decay constant. For doing this, a non-perturbative matching of parameters in the lattice heavy quark effective theory, and in this project we choose a two-step strategy : (1)construction of relativistic lattice action on an anisotropic lattice, and (2)matching onto the heavy quark effective theory.For the anisotropic lattice action on the lattice, there was a worry that it produces large systematic error when used for heavy quarks. We propose an action which does not have such a problem. That is based on a lattice fermion action including interactions with next-to-nearest neighbors. We confirmed that the problem does not appear by perturbative calculations. In addition we calculated the non-perturbative matching of the parameters in the anisotropic lattice action in order to make it consistent with the Lorentz symmetry.For the heavy quark effective theory, we consider an action that contains 1/m corrections, and started a work to do a non-perturbative matching calculation using the Schrodinger functional technique. It is based on the method already available in the case of the static approximation which contains no 1/m corrections.