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

这项工作旨在使用晶格上量子染色体动力学的大规模数值模拟，旨在阐明从强子相到夸克面筋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。在项目的第一年，我们研究了相变本身的属性。在项目的第二年和第三年中，我们计算了代表有关等离子体阶段的基本信息的状态方程。我们获得的主要结果如下1。为了理解现实世界中的有限温度相变，了解向上和向下Quark M_ <ud>的质量差异以及奇怪的Quark M_S的质量差异会影响相变的性质。我们使用Kogut-susskind Quark Action对（M_ <ud>，M_S）平面（M_ <ud>，m_s）平面上的相变线进行了系统的确定，并确定了关键的夸克质量以外的关键夸克质量……更多的是一阶相变的不存在。对SU（3）对称情况的进一步研究表明，一阶转变的终点是二阶过渡点，并且Sigma粒子在此点变得无质量。2。夸克gluon等离子体阶段状态方程的过去计算仅使用了Kogut-susskind Quark动作。在我们的工作中，我们采用了威尔逊式的夸克动作，它比自旋味含量中的kogut-susskind Quark Action自然得多。由于此计算是CPU时间密集的，因此是一个完整的QCD计算，我们已经探索了用于Glut和Quark扇区的改进动作的使用。我们采用了国家计算的积分方法。为了进行方法论，我们首先计算了纯仪表理论的状态方程，并确定了能量密度和压力的温度依赖性。按照持续的限制，我们获得了状态方程的结果，这与标准PLQQuette Action的状态相一致。对于完整的QCD，我们首先确定了（K，β）平面上的相图，以识别奇偶校验破裂的区域和临界线。然后，我们对临时晶格尺寸N_1 = 4和6进行模拟，而间隙大于16^3。探索了与M_π/M_ρ= O.6-0.95相对应的夸克质量区域，并确定能量密度和压力是温度和夸克质量的函数。这些结果中发现的主要特征是（i）一旦夸克质量降至m_π/m_ρ= 0.9，并且（ii）n_1 = 6结果显示，与持续的stefan-boltzmann值高于t/ t_1 = 2的结果大致一致。需要进一步的研究来确认和扩展这些结果，特别是使用较大临时尺寸的晶格进行缩放研究。较少的

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)