Study on the character of elementary excitations around critical point of QCD phase transitions

我们已经证明，由于与手性软模式的耦合，有限温度下手性转变周围的夸克可以改变其准粒子图像。在临界点附近，可能会出现与相变阶次参数波动耦合的软​​模。我们研究了有限温度下这种玻色子模式引起的夸克自能。我们已经证明，夸克的谱函数在低能区域具有三个峰值：其中两个存在于正能量区域和负能量区域，对应于在极高温度区域有效的硬热循环近似中常见的正常夸克和等离子体激发。我们已经证明，存在能量微乎其微的附加激发。我们从夸克和热激发反夸克之间的能级交叉的角度阐明了这种多峰结构的形成机制。我们还表明，三峰结构的这种实现不依赖于玻色子激励的类型，即，它可以是矢量或轴向矢量类型。我们还确定了与三个峰值相对应的极点，并检查了极点的温度依赖性。我们发现，当夸克质量增加时，这三个轨迹的集合会急剧改变其结构。我们尝试使用所谓的重正化群方法来构造粘性流体的合​​理流体动力学方程。我们已经证明，与原始埃卡特方程不同，所获得的粒子系方程并未表现出病态行为。

We have shown that the quarks around the chiral transition at finite temperature can change their quasi-particle picture owing to the coupling to the chiral soft modes. Around the critical point, there may appear soft modes which are coupled to the fluctuations of the order parameter of the phase transition. We have investigated the quark self-energy due to this bosonic mode at finite temperature. We have shown that the spectral function of the quark gets to have three peaks in the low-energy region : The two of them existing in the positive-and negative-energy regions correspond to the normal-quark and plasmino excitations familiar in the hard-thermal loop approximation valid in the extremely high-temperature region. We have shown that there appears an additional excitation with a vanishingly small energy. We have clarified the mechanism for the formation of such a multiple peak structure in terms of the level crossing between the quark and the thermally excited anti-quarks. We have also shown that such a realization of the three-peak structure does not depend on the type of the bosonic excitation, i.e., it may be vector or axial vector type. We have also identified the poles corresponding to the three peaks, and examined the temperature dependence of the poles. We have found that the set of the three trajectories changes its structure in a drastic way when the quak mass is raised.We have tried to construct sensible hydrodynamic equations for viscous fluids using the so called renormalization-group method. We have shown that the obtained equation in the particle fame does not show a pathological behavior unlike to the original Eckart equation.