Study of the QCD phase diagram - Understanding of high-energy heavy ion collisions based on the first principle calculation and phenomenology

我们的主要目的是从高能重离子碰撞的角度研究QCD相变的动力学和夸克胶子等离子体（QGP）的详细性质。在2000年开始运行的相对论重离子对撞机（RHIC）上，实现了强相互作用QGP（sQGP）的产生。根据相对论流体力学和复合模型，通过对实验数据的理解，建立了在RHIC上产生sQGP的理论。此外，在大型强子对撞机（LHC）上，重离子碰撞的操作于2010年开始。为了从RHIC和LHC的高能重离子碰撞中了解QGP性质，我们进行了唯象研究。首先，我们将QGP的粘性效应引入到Hydro + UrQMD模型中，该模型不仅能描述碰撞后产生的热密物质的流体动力学膨胀，而且能描述强子之间的末态相互作用。在这里，我们开发了一个新的算法，这是基于Godfred方法求解相对论粘性流体动力学方程。我们的数值方法具有以下重要性质：（i）小的数值耗散，这对于分析实验数据中的物理粘性是重要的。(ii)用于处理逐事件初始波动的激波捕获方案。结果表明，该数值格式比其他算法（SHASTA，KT和NT）具有更小的数值耗散。我们评估包含我们的算法的数值耗散。现在我们将该算法推广到三维计算，并利用我们的新流体动力学程序对RHIC和LHC进行了实际计算。

Our main purpose is to investigate the dynamics of the QCD phase transition and detailed property of Quark-gluon plasma (QGP) from the point of view of analyses of high-energy heavy ion collisions. At the Relativistic Heavy Ion Collider (RHIC) which started its operation in 2000, the production of the strongly interacting QGP (sQGP) was achieved. The production of the sQGP at RHIC was established by understanding of experimental data based on relativistic hydrodynamics and the recombination model. Furthermore, at Large Hadron Collider (LHC) the operation of heavy ion collisions started in 2010. To get insight of QGP property from understanding of high-enegy heavy ion collisions at RHIC and LHC, we carried out phenomenological studies. First we include the viscosity effect of QGP into thehydro + UrQMD model which can describe not only the hydrodynamic expansion of hot and dense matter that is created after collisions but also final state interactions among hadrons. Here we developed a new algorithm that is based on the Godunov method for solving the relativistic viscous hydrodynamic equation. Our numerical method has the following important properties; (i) small numerical dissipation which is important for analyses of physical viscosity in experimental data. (ii) shock-wave capturing scheme for dealing with event-by-event initial fluctuations. We show that our numerical scheme has advantages over than other algorithms (SHASTA, KT and NT) in having smallnumerical dissipation. We evaluate the numerical dissipation that contains our algorithm. Now we extend the this algorithm to 3-dimentional calculation and start a realistic calculation for RHIC and LHC using our new hydrodynamic code.