NUMERICAL STUDY OF LATTICE QCD WITH THREE DYNAMICAL QUARKS

这项工作旨在发展包括动力学奇异夸克和动力学上夸克和下夸克在内的格子QCD模拟方法。我们所取得的主要结果如下：1.算法开发处理奇数个动力学夸克需要一个算法开发。我们已经证明，多项式HMC，其中奇异夸克所需的单个狄拉克算符的逆用多项式近似，为这一目的提供了一种可行的方法。我们还将该算法推广到Kogut-Susskind作用，并给出了它的精确PHMC算法，这样的精确算法在以前是未知的。三味晶格QCD的相结构我们应用该算法研究了有限晶格间距下三味晶格QCD的相结构。发现斑块和三叶草夸克作用的组合形成了一条一级相变线，这是一种晶格伪影。当过渡在…之前终止时当更多的矿石达到连续极限时，终止点处的晶格间距约为4GeV。由于我们需要开始更接近连续体极限的模拟，以避免这种相变的非物理影响，因此牌匾-三叶草的组合对于进行实际模拟似乎是不现实的。将规范作用量转换为RG改进作用量，发现相变消失，这可能是因为改进作用量使规范场涨落更接近于连续。RG改进规范作用的三叶草系数的确定要使用晶格间距1/a=1-2GeV进行连续统外推，需要O(A)改进作用。由于RG改进规范作用的三叶草系数是未知的，因此我们决定采用薛定谔泛函方法。结果表明，由于裸规范耦合很大，因此需要精确控制O(a/L)误差。我们用固定的L(以物理单位表示)模拟来处理这个问题，并确定了三叶草系数作为裸规耦合的函数。物理运行作为迈向现实三味QCD模拟的第一步，我们已经开始使用16^3x32晶格在L/a=2GeV上运行。我们计划进行轻强子谱运行，然后测定轻夸克质量和QCD耦合常数。关于重夸克物理的进一步工作将利用在这些研究中产生的规范组态。较少

This work aimed to develop methods for lattice QCD simulations including dynamical strange quark in addition to dynamical up and down quarks. The main results we have obtained are as follows.1. Algorithm developmentTreating odd number of dynamical quarks requires an algorithmic development. We have shown that the polynomial HMC, in which the inverse of a single Dirac operator needed for the strange quark is approximated by a polynomial, provides a viable method for this purpose. We have also extended the algorithm to the Kogut-Susskind action, and has formulated an exact PHMC algorithm for it; such an exact algorithm had not been known before.2. phase structure of three-flavor lattice QCDWe have applied the algorithm to study the phase structure for three-flavor lattice QCD at finite lattice spacings. It was found that the combination of the plaquette and clover quark action develops a line of first-order phase transition which is a lattice artifact. While the transition terminates bef … More ore reaching the continuum limit, the lattice spacing at the termination point turned out to be about 4GeV. Since we need to start simulations closer to the continuum limit to avoid unphysical effects of such phase transitions, the plaquette-clover combination appears impractical for carrying out actual simulations. Switching the gauge action to an RG-improved action, it was found that the phase transition disappears, presumably because gauge field fluctuation becomes more continuum-like for improved actions.3. Determination of the clover coefficient for RG-improved gauge actionTo carry out a continuum extrapolation using lattice spacing 1/a=1-2GeV, an O (a) improved action is needed. Since the clover coefficient for the RG-improved gauge action is not known, we have decided to apply the Schrodinger functional method for this purpose. It turned out that O(a/L) errors need to be controlled precisely for this purpose, since bare gauge coupling is large. We treated this problem through simulations with a fixed L(in physical units), and determined the clover coefficient as a function of the bare gauge coupling.4. Physics runsAs a first step toward realistic three flavor QCD simulations, we have started runs at l/a=2GeV using 16^3x32 lattices. We plan to carry out the light hadron spectrum run, followed by determinations of light quark masses and the QCD coupling constant. Further work on heavy quark physics shall utilize gauge configurations generated in those studies. Less