NUMERICAL STUDY OF FINITE-TEMPERATURE LATTICE QCD

本工作旨在阐明从强子相到夸克胶子等离子体相的相变性质，以及由此产生的高温相的物理性质，利用大规模量子色动力学在晶格上的数值模拟。在项目的第一年，我们研究了相变本身的性质。在项目的第二年和第三年，我们计算了代表等离子体相基本信息的状态方程。我们得到的主要结果如下。为了理解现实世界的有限温度相变，了解上下夸克m_<ud>和奇夸克m_s的质量差如何影响相变的性质是非常重要的。我们利用Kogut-Susskind夸克作用对（m_<ud>, m_s）平面上的相变线进行了系统的测定，并确定了一阶相变不存在的临界夸克质量。对SU(3)对称情况的进一步研究表明，一阶跃迁的终点是一个二阶跃迁点，并且sigma粒子在该点变得无质量。过去对夸克胶子等离子体相的状态方程的计算只使用了Kogut-Susskind夸克作用。在我们的工作中，我们采用了威尔逊型夸克作用，这种夸克作用在自旋风味物质中比Kogut-Susskind夸克作用更自然。由于这个计算是CPU时间密集型的，作为一个完整的QCD计算，我们已经对胶子和夸克扇区都使用了改进的动作。我们采用积分法计算状态方程。作为方法准备，我们首先计算了纯规范理论的状态方程，并确定了能量密度和压力的温度依赖性。在连续统极限下，得到的状态方程与标准血小板作用的结果在3%以内一致。对于全QCD，我们首先确定了（K,β）平面上的相图，确定了宇称破相区域和临界线。然后，我们在时间格尺寸N_1=4和6，空间格尺寸大多为16^3的格上进行了模拟。探索了夸克质量m_π/m_ρ= 0.6 -0.95的区域，并确定了能量密度和压力是温度和夸克质量的函数。在这些结果中发现的主要特征是：(i)当夸克质量低于m_π/m_ρ=0.9时，只看到弱依赖；（ii） N_1=6的结果与T/ T_1=2以上的连续体Stefan-Boltzmann值大致一致。需要进一步的研究来证实和扩展这些结果，特别是需要使用更大时间尺度的格进行尺度研究。少

This work aimed to elucidate the nature of the phase transition from hadron phase to quark gluon plasma phase, and physical properties of the consequent high temperature phase, using large-scale numerical simulations of quantum chromodynamics on the lattice. In the first year of the project, we investigated the properties of the phase transition itself. In the second and third years of the project, we calculated the equation of state which represent the fundamental information concerning the plasma phase. The main results we have obtained are as follows.1. For understanding the finite-temperature phase transition of the real world, it is very important to learn how the difference of masses of the up and down quark m_<ud> and that of the strange quark m_s affects the nature of the phase transition. We have carried out a systematic determination of the line of phase transition on the (m_<ud>, m_s) plane using the Kogut-Susskind quark action, and identified the critical quark mass beyond … More which the first-order phase transition becomes absent. Further investigation of the SU (3) symmetric case has shown that the end-point of the first-order transition is a second-order transition point, and that the sigma particle becomes massless at that point.2. Past calculations of the equation of state of the quark gluon plasma phase has exclusively used the Kogut-Susskind quark action. In our work we employed the Wilson-type quark action which is far more natural than the Kogut-Susskind quark action in the spin-flavor content. Since this calculation is CPU time intensive, being a full QCD calculation, we have exploited the use of improved actions both for the gluon and quark sectors. We adopted the integral method for calcuation of equation of state. For a methodological preparation, we first calculated the equation of state for pure gauge theory, and determined the temperature dependence of energy density and pressure. Taking the continuum limit, we obtained results for the equation of state which are in agreement with those of the standard plqquette action within 3%. For full QCD, we first determined the phase diagram on the (K,β) plane, identifying the region of parity broken phase and the critical line. We then carried out simulations on lattices with the temporal lattice size N_1=4 and 6 and the spatical size mostly 16^3. The region of quark masses corresponding to m_π/m_ρ=O.6-0.95 were explored, and the energy density and pressure were determined as a function of temperature and quark mass. The main features found in these results are (i) only weak dependence is seen once quark mass falls below m_π/m_ρ=0.9, and (ii) N_1=6 results show an approximate agreement with the continuum Stefan-Boltzmann values above T/ T_1=2. Further studies are needed to confirm and extend these results, in particulr to carry out scaling study using lattices with larger temporal sizes. Less