Research on the coupling constant and its scale dependence via lattice QCD simulations

本项目的目的是通过点阵QCD模拟计算耦合常数的尺度依赖性，耦合常数是QCD的基本参数之一。我们对胶子使用RG改进的规范作用，对夸克使用非微扰改进的威尔逊费米子作用。用薛定谔泛函方法计算了耦合常数的阶跃尺度函数，以评价耦合常数的尺度依赖性。作为第一步，在微扰理论中，对于RG规范作用的一种情况，确定了边界项在1环处的改进系数。在淬火QCD模拟中验证了该系数的确定方法。然后，我们确定了在薛定谔函数设置中费米子作用的改进项的三叶草系数。此外，利用薛定谔泛函方法估计了各种算子的重整化常数和改进系数。另一方面，我们在2+1味全QCD模拟中计算了强子光谱，以确定低能量尺度。提出了一种新的控制Wilson型夸克手性外推的理论方法——Wilson手性微扰理论，并利用该方法计算了不同数量的夸克质量依赖关系。我们测试了一种新的光动力学夸克算法，称为域分解HMC算法，用于物理夸克质量下的晶格QCD模拟。对3味QCD中的SSF进行了评价，并对2+1味QCD中的强子谱进行了计算。

A purpose of this project is to calculate a scale dependence of the coupling constant, which is one of fundamental parameters in QCD, by lattice QCD simulations. We use a RG improved gauge action for gluons and a non-perturbatively improved Wilson fermion act ion for quarks. A step scaling function of the coupling constant is calculated by the Schrodinger functional method to evaluate the scale dependence of the coupling constant. As a first step, an improvement coefficient for a boundary term is determined at 1 loop in perturbation theory for a case of the RG gauge act ion. This determination of the coefficient is tested in quenched QCD simulations. We then have determined the clover coefficient for an improved term in the fermion action non-perturbatively in the Schrodinger functional setup. In addition, renormalization constants as well as improved coefficients for various operators are estimated by the Schrodinger functional method. On the other hand, we have calculated hadron spectra in 2+1 flavor full QCD simulations, in order to determine a low energy scale. A new theoretical method, called Wilson chiral perturbation theory, is proposed to control chiral extrapolations for Wilson type quarks and quark mass dependences for various quantities are calculated by this method. We have tested a new algorithm for light dynamical quarks, called domain-decomposed HMC algorithm, towards lattice QCD simulations at physical quark mass. An evaluation of SSF in 3 flavor QCD and a calculation of hadron spectra in 2+1 flavor QCD are now under way.