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

本研究项目的目的是建立晶格上的重夸克有效理论，这是模拟晶格QCD中的重夸克所必需的。利用这种公式，可以减少各种B介子矩阵元的晶格计算中的系统不确定性，如B介子衰变常数。为此，对晶格重夸克有效理论中的参数进行了非微扰匹配，在本项目中我们选择了两步策略：(1)构造各向异性晶格上的相对论晶格作用量，和(2)匹配到重夸克有效理论上。对于晶格上的各向异性晶格作用量，人们担心它在用于重夸克时会产生很大的系统误差。我们建议采取一项不存在此类问题的行动。这是基于格子费米子作用，包括与次近邻的相互作用。我们通过摄动计算证实了这个问题没有出现。此外，我们还计算了各向异性晶格作用中参数的非微扰匹配，以使其与洛伦兹对称性一致。对于重夸克有效理论，我们考虑了一个包含1/m修正的作用，并开始了利用薛定谔泛函技术进行非微扰匹配计算的工作。它基于静态近似中已有的方法，静态近似不包含1/m修正。

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.