Renormalization group transformation in lattice QCD with quarks

本项目旨在利用重正化群方法研究动态夸克在量子色动力学（QCD）中的改进作用。由于晶格作用的规范部分在晶格间距为a的情况下引入了O（a^2）的晶格伪迹，因此人们认为改进夸克部分，使其与标准威尔逊费米子作用有O(a)的误差，可能会在数值模拟中消除大部分晶格伪迹。然而，最具问题的晶格伪影，即晶格上的手性对称性的破坏，是由于倍增子造成的，其影响不能通过α中的朴素序计数来估计。为了抑制物理观测中倍频器的污染，背景测量配置中的最大动量应该很小。在这里，我们注意到重整化群（RG）变换直接抑制了这种高动量模式。因此，与赛门铁克改进计划的情况不同，该计划基于α中的朴素功率计数，我们期望rg改进的规范行动能够有效地抑制由于加倍而产生的晶格伪像。我们研究了rg改进的规范作用和三叶草改进的夸克作用的组合。通过对改进和标准动作的系统比较研究，我们发现规范部分和夸克部分都需要改进。然后，我们开始将我们的改进行动组合应用于轻强子质量谱，轻夸克质量，静态夸克势，U(1)问题，包括重夸克，b和c在内的强子的衰变常数和质量谱问题，并进行了包括连续统外推在内的完整QCD中强子性质的第一次系统研究。我们还研究了有限温度下QCD的状态方程。这些研究证实了动力学夸克的重要性，以及动力学改进的重要性。

This project aims at a research of improved actions in quantum chromodynamics (QCD) with dynamical quarks, using the renormalization group method. Because the gauge part of the lattice action introduce lattice artifacts of O(a^2), with a the lattice spacing, it has been considerd that an improvement of the quark part, which has O(a) errors with the standard Wilson fermion action, might remove the major prt of the lattice artifacts in numerical simulations. However, the most problematic lattice artifact, the violation of the chiral symmetry on the lattice, is due to the doublers, whose effects cannot be estimated by a naive order counting in α. In order to suppress the contamination of doublers in physical observables, the maximum momentum in the background gauge configuration should be small. Here, we note that a renormalization group (RG) transformation directly suppress such high momentum modes. Therefore, unlike the case of Symanzik improvement program which is based on a naive power counting in α, we expect that a RG-improved gauge action is efficient to suppress lattice artifacts due to doublers. We study the combination of a RG-improved gauge action and a clover-improved quark action.From a systematic comparative study of improved and standard actions, we found that improvement is necessary both for the gauge and quark parts. We then started to apply our combination of improved actions to the problems of light hadron mass spectrum, light quark mass, static quark potential, the U (1) problem, decay constants and mass spectrum for hadrons including heavy quarks, b and c, and performed the first systematic study of hadron properties in full QCD including a continuum extrapolation. We also studied the equaton of state for QCD at finite temperature. From these studies, importance of dynamical quarks, and also of action improvements, is confirmed.