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

我们证明了在有限温度下，手征跃迁附近的夸克由于与手征软模的耦合，可以改变它们的准粒子图象。在临界点附近，可能出现软模，软模与相变序参量的涨落相耦合。我们研究了有限温度下这种玻色子模引起的夸克自能。我们已经证明，夸克的谱函数在低能区有三个峰：其中两个峰存在于正能区和负能区，对应于在极高温区有效的硬热环近似中常见的正常夸克和等离子体激发。我们已经表明，出现了一个附加的激发，其能量非常小。我们从夸克和热激发反夸克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，这种三峰结构的实现不依赖于玻色子激发的类型，即，它可以是矢量型或轴向矢量型。我们还确定了对应于三个峰值的极点，并研究了极点的温度依赖性。我们发现，当夸克质量增加时，三条轨迹的集合结构发生了剧烈的变化。我们试图用重整化群方法构造粘性流体的合理流体动力学方程。我们已经表明，在粒子的框架中得到的方程不显示出不同于原来的Eckart方程的病态行为。

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.