NUMERICAL STUDY OF FINITE-TEMPERATURE LATTICE QCD

有限温晶格QCD的数值研究

• 批准号: 10640246
• 负责人: UKAWA Akira
• 金额: $ 1.73万
• 依托单位: UNIVERSITY OF TSUKUBA
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640246/
• 关键词: QUARK GLUON PLASMA; LATTICE QCD; FINITE TEMPERATURE; FINITE DENSITY; LATTICE GAUGE THEORY; NUMERICAL SIMULATION; HIGH ENERGY HEAVY ION SCATTERING; EARLY UNIVERSE; クォーク・グルオL・プラズマ; 量子色力学; 相転移; 状態方程式; クォークゲルオンプラズマ

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

这项工作的目的是阐明从强子相到夸克胶子等离子体相的相变的性质，以及随之而来的高温相的物理性质，使用大规模的量子色动力学数值模拟的晶格。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，我们计算了状态方程，它代表了有关等离子体相的基本信息。主要结果如下：1.为了理解真实的世界的有限温度相变，了解上、下夸克m_s和<ud>奇异夸克m_s的质量差对相变性质的影响是非常重要的。我们用Kogut-Susskind夸克作用量系统地确定了（m_<ud>，m_s）平面上的相变线，并确定了临界夸克质量 ...更多信息 一阶相变消失。对SU（3）对称情形的进一步研究表明，一级跃迁的终点是一个二级跃迁点，并且σ粒子在该点处变得无质量.过去对夸克胶子等离子体相状态方程的计算只使用了Kogut-Susskind夸克作用量。在我们的工作中，我们采用了Wilson型夸克作用量，它比Kogut-Susskind夸克作用量的自旋味含量更自然。由于这种计算是CPU时间密集型的，是一个完整的QCD计算，我们已经利用了改进的行动都胶子和夸克部门的使用。采用积分法计算状态方程。作为方法上的准备，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。在连续极限下，我们得到的状态方程结果与标准Plqquette作用量的结果在3%以内符合。对于全QCD，我们首先确定了（K，β）平面上的相图，确定了宇称破缺相的区域和临界线。然后，我们进行了模拟的时间晶格大小N_1=4和6和空间大小主要是16^3的格子。探索了m π/m ρ= 0.6 -0.95的夸克质量区域，确定了能量密度和压强随温度和夸克质量的变化关系。这些结果的主要特点是：（i）当夸克质量福尔斯降到m_π/m_ρ=0.9以下时，只观察到弱的依赖性;（ii）N_1=6的结果与T/ T_1=2以上的Stefan-Boltzmann连续谱值近似一致。这些结果还需要进一步的研究来证实和推广，特别是在时间尺度更大的格子上进行标度研究。少

项目成果

Taku Izubuchi, Junichi Noaki, Akira Ukawa: "Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential"Phys. Rev.. D58. 114507 (1998)

Taku Izubuchi、Junichi Noaki、Akira Ukawa：“有限温度和化学势下具有威尔逊费米子作用的二维晶格 Gross-Neveu 模型”Phys。

T.Izubuchi et al.: "Two-dimensional lattice Grass-Neuen model with Wilson action at finite temperature and chemical potential" Phys.Rev.D. 58. M4507-1-M4507-12 (1998)

T.Izubuchi 等人：“有限温度和化学势下具有 Wilson 作用的二维晶格 Grass-Neuen 模型”Phys.Rev.D。

Y.Aoki,F.Csikor,Z.Fodor,A.Ukawa: "The endpoint of the first-order phase transition of the SU(2) gauge-Higgs model on a 4-dimensional isotropic lattice"Physical Review D. 60. 013001 (1999)

Y.Aoki、F.Csikor、Z.Fodor、A.Ukawa：“4 维各向同性晶格上 SU(2) 规范希格斯模型的一阶相变的终点”物理评论 D. 60。

A.Ali Khan: "Equation of state for pure su(3) guage theory with RG improred action"Nucl Physics B (proc.Suppl.). 印刷中.

A.Ali Khan：“具有 RG 改进作用的纯 su(3) 规范理论的状态方程”核物理 B（proc.Suppl.）正在出版。

Y.Aoki: "The end point of the first-order phase transition of the su(2) gauge-Higgs model on a 4d lattice"Physical Review D. 60. 1-8 (1999)

Y.Aoki：“4d 晶格上 su(2) 规范希格斯模型的一阶相变的终点”物理评论 D. 60. 1-8 (1999)