First-Principle Calculation of Hadron System at finite Temperature

夸克和胶子有一个特殊的特性，即“约束”。它们的动力学QCD预测了高温下约束的破坏。这种状态被称为“夸克-胶子等离子体（QGP）”，是在宇宙的早期阶段实现的。近年来，欧洲和美国广泛开展高能重离子实验来寻找QGP。在这个项目中，我们在德国和日本之间交换了研究人员，讨论了有限温度下强子的行为，有限密度系统的计算算法，并开发了用于有限温度研究的各向同性晶格。我们得到了以下结果：1。阐明了极点质量与虚时间两点函数之间的关系。然后用点阵QCD测量了极化质量和屏蔽质量，并分析了它们与温度的关系。我们分析了各向同性晶格，以获得沿温度方向的高分辨率。我们扩大了研究范围，包括改进压力表动作。为了研究早期宇宙和高能重离子碰撞时的系统，我们需要分析有限密度的方法。由于有限化学势的晶格QCD计算是一项非常困难的任务，因此之前已经做了一些试验。我们从强子质量对化学势的响应和颜色SU(2)理论来解决这个问题。在重归一化的轨迹上，由于离散化导致的点阵伪影有望消失。对SU(3)规范系统进行了非摄动的重整化变换，得到了重整化轨迹。

Quarks and gluons have a peculiar feature, i.e., "Confinement". Their dynamics, QCD, predicts the violation of the confinement at high temperature. Such state is called "Quark-Gluon Plasma (QGP)", and was realized at the early stage of the universe. Recently high energy heavy ion experiments have been performed extensively in Europe and USA to search for QGP.In this project, we exchanged researchers between Germany and Japan to discuss the behavior of hadrons at finite temperature, calculational algorithms for finite density systems, and to develop an-isotropic lattice for finite temperature study. We have obtained the following results :1. The relation between the pole masses and two-point functions of imaginary time has been clarified. Then we measured the pole and screening masses by lattice QCD and showed their temperature dependence.2. We have analyzed an-isotropic lattice to get high resolution along the temperature direction. We have extended the study to include improved gauge actions.3. To study the system at the early universe and high energy heavy ion collisions, we need to method to analyze the finite density. Because lattice QCD calculation with finite chemical potential is very hard task, a few trials had been done before. We approach the problem from the response of hadron masses with respect to the chemical potential, and color SU(2) theory.4. On the renormalized trajectory, it is expected that the lattice artifact due to the discretization disappears. We have done the renormalization transformation for SU(3) gauge system non-perturbatively, and found the renormalized trajectory.