夸克物质的色介电函数及喷注在介质中的感应现象
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摘要
量子色动力学(QCD)预测在高温高密下,强子物质会发生退禁闭相变,形成一种新的物质形态——夸克胶子等离子体(QGP)。理论研究表明,采用相对论重离子碰撞的实验手段,在很小的空间范围内可以达到、超过退禁闭相变发生时的临界温度Tc。相对论重离子对撞机(RHIC)于2000年建成投入运行,至今已经取得很重要的发现。虽然目前还存在着争议,但很多物理学家认为在RHIC上已经产生了QGP。不过与人们所预测的弱耦合的QGP不同,而是一种低粘滞强相互作用的近理想QGP流体。因此,对QGP性质的认识了解还有待进一步的研究。本论文主要研究QGP的色介电函数、喷注在QGP中穿过时在介质中激发的感应现象。
首先,我们简单地介绍RHIC上的一些重要发现,如椭圆流(v2),喷注淬火(jet quenching),双强子方位角关联等。随后介绍研究夸克物质的理论基础,包括有限温度场论、动力论、流体力学等等。
在硬热圈重求和方法下,我们计算了QGP中硬胶子极化导致的介电函数。结果显示介电函数的实部在类空区间有非平庸的极值结构,对应实部出现极值结构的w/k处,虚部也表现出共振吸收行为。这意味着重求和计算的介电函数在此区间的极值表现同类空区间的一种能量交换机制一朗道阻尼相关。重求和计算的贡献主要来自于胶子的自相互作用,也就是三胶子、四胶子相互作用。这些非线性非阿贝尔相互作用会导致QGP中的非线性朗道阻尼,从而决定了介电函数实虚部在此区间的性质。
应用硬热圈重求和方法得到的介电函数,在线性响应理论下,我们讨论了快速部分子穿过QGP时引起的尾迹势(wake potential)。在向后方向上,当快速部分子速度为v=0.55c时,尾迹势是Lennard-Jones势；而v=0.99c时,尾迹势表现出明显的振荡行为。而在向前方向上,无论v=0.55c还是v=0.99c,都是改进的库伦势。相比于用硬热圈近似的介电函数计算的结果,来自于重求和计算的非线性非阿贝尔效应显著增加了尾迹势在向前—向后方向上的不对称性。详细的讨论表明,尾迹结构的特征性质主要由介电函数的虚部决定。
当QGP中有切向粘滞时,根据动力论方程和切向粘滞修正的分布函数,我们推导出粘性色流体力学方程；并根据这些方程求解出极化张量和介电函数。当η/s很小时,如1/4π,介电函数的实部轻微地偏离理想色流体η/s=0的结果。随着η/s的增大,它们之间的偏离逐渐变大。同时,介电函数的虚部也表现出类似的性质。另外,在一些确定的模式w/k下,实部或虚部中所有的粘性曲线和理想曲线都相交于一点。这意味着在这些模式下,介电函数的实部或虚部跟切向粘滞无关。
我们应用粘性色流体方程计算的粘性介电函数,在线性响应近似下,计算了快速部分子在粘性QGP中运动时引起的尾迹势。通过介电函数,切向粘滞影响着尾迹势。数值结果表明,切向粘滞对尾迹势的影响跟快速部分子的运动速度相关系。v=0.99c时,相比于理想色流体力学的结果,粘滞效应使尾迹势的振荡行为变得更加显著。而当v=0.55c时,从数值结果上来看,切向粘滞对尾迹势的影响非常微小,所有的粘性势曲线同理想曲线都重叠在一起,所有的曲线间没有明显的差异。结合切向粘滞对介电函数的影响,以及介电函数对尾迹势的决定性作用,我们讨论解释了这种粘滞效应对尾迹势的速度相关的影响。
Quantum chromodynamics (QCD) predicts that deconfined phase transition will take place at high temperature and/or high density. As a result, the nuclear matter will undergo a transition to quark-gluon plasma (QGP) which is composed of quarks and gluons. Many theoretical studies indicate that the expected high temperature will reach by colliding two ultrarelativistic heavy nuclei at sufficiently high energy in laboratory. One main goal for the Relativistic Heavy Ion Collider (RHIC) is to seek this new state of matter. RHIC have provide several different colliding systems at a variety of energies and the vast data have been collected since its operation in 2000. Though there are controversies, many physicists argue that the QGP is produced at RHIC. However, it is not a long expected weak coupled QGP, but a strongly coupled and nearly perfect quark gluon fluid with a very small viscosity. To study global properties of the QGP is an urgent topic in heavy ion community. In this thesis, we focus on the color dielectric function of the QGP and the phenomena induced by a fast parton traveling through the QGP.
At first, we will briefly introduce some primary findings at RHIC, such as, elliptic flow v2, jet quenching and azimuthal dihadron correlation observable. Then, we will review foundations of finite temperature field theory, kinetic theory and hydrodynamics which are theoretical tools for the QGP.
With the hard thermal loop (HTL) resummation technique, we calculate the dielectric function excited by hard gluon in the quark-gluon plasma. We find that in the space-like regionω/k< 1, the real part of the dielectric function has two nontrivial extremum structures. At the same time, at theω/k where the extrema of the real part are located, the imaginary part of the dielectric function shows resonance structures. While the real and imaginary parts of dielectric function in the HTL approximation are both monotonously in the space-like region, showing no any resonance structures. These facts imply that properties of the dielectric function in the space-like region relate to some energy exchange mechanism—Landau damping. The main contributions of the resummation calculation come from the three and four gluon interactions which reflect nonlinear and non-Abelian nature of the quark-gluon plasma. Nonlinear and non-Abelian interaction will result in nonlinear Landau damping, which determines the properties of the dielectric function in the space-like region.
Within the framework of the linear response theory, by applying the dielectric function calcu- lated with the HTL resummation technique, we study the wake potential induced by a fast parton traveling through the QGP. In the backward direction, wake potential is a Lennard—Jones poten-tial at v= 0.55c, while the wake potential shows an obvious oscillatory behavior for v= 0.99c. In the forward direction, it is a modified Coulomb potential for both cases of v= 0.55c and v= 0.99c. In comparison with results calculated with the HTL dielectric function, nonlinear and non-abelian effects from the resummation calculation enhance anisotropy of the wake potential in the backward-forward directions. Finally, we give some explanations for those wake properties.
Viscosity will modify the distribution functions of quark and gluon. By using quark dis-tribution function modified by shear viscosity, we derive the viscous chromohydrodynamics by expanding the kinetic equation in momenta moments and truncating the expansion at the second moment level. In terms of the viscous chromohydrodynamic equations, we can derive the polar-ization tensor and the dielectric function. Whenη/s is small, such as the AdS/CFT bound 1/4π, the real part of the dielectric function deviates from the ideal chromohydrodynamic case (η/s= 0) slightly. With the increase ofη/s, its deviation becomes larger. Meanwhile, the imaginary part exhibits the similar properties. In addition, at some modes ofω/k, the real and the imaginary parts are independent on the shear viscosity. By analyzing the mathematical structures of the dielectric function, we give some explanations for the behavior.
By using the viscous dielectric function, we calculate the wake potential induced by a fast parton traveling through the viscous QGP. Through the dielectric function, shear viscosity af-fects the wake potential. The numerical analysis shows that viscous effects on wake potential are speed-dependent. In comparison with the ideal chromohydrodynamic results, shear viscosity make oscillation of wake potential more pronounced at v= 0.99c. While v= 0.55c, the viscous effects on the wake potential are so trivial in both the forward and backward directions and one can hardly distinguish all viscous potential curves from each other. Finally, we give some explanations for the speed-dependent viscous effects on the wake properties.
首先,我们简单地介绍RHIC上的一些重要发现,如椭圆流(v2),喷注淬火(jet quenching),双强子方位角关联等。随后介绍研究夸克物质的理论基础,包括有限温度场论、动力论、流体力学等等。
在硬热圈重求和方法下,我们计算了QGP中硬胶子极化导致的介电函数。结果显示介电函数的实部在类空区间有非平庸的极值结构,对应实部出现极值结构的w/k处,虚部也表现出共振吸收行为。这意味着重求和计算的介电函数在此区间的极值表现同类空区间的一种能量交换机制一朗道阻尼相关。重求和计算的贡献主要来自于胶子的自相互作用,也就是三胶子、四胶子相互作用。这些非线性非阿贝尔相互作用会导致QGP中的非线性朗道阻尼,从而决定了介电函数实虚部在此区间的性质。
应用硬热圈重求和方法得到的介电函数,在线性响应理论下,我们讨论了快速部分子穿过QGP时引起的尾迹势(wake potential)。在向后方向上,当快速部分子速度为v=0.55c时,尾迹势是Lennard-Jones势；而v=0.99c时,尾迹势表现出明显的振荡行为。而在向前方向上,无论v=0.55c还是v=0.99c,都是改进的库伦势。相比于用硬热圈近似的介电函数计算的结果,来自于重求和计算的非线性非阿贝尔效应显著增加了尾迹势在向前—向后方向上的不对称性。详细的讨论表明,尾迹结构的特征性质主要由介电函数的虚部决定。
当QGP中有切向粘滞时,根据动力论方程和切向粘滞修正的分布函数,我们推导出粘性色流体力学方程；并根据这些方程求解出极化张量和介电函数。当η/s很小时,如1/4π,介电函数的实部轻微地偏离理想色流体η/s=0的结果。随着η/s的增大,它们之间的偏离逐渐变大。同时,介电函数的虚部也表现出类似的性质。另外,在一些确定的模式w/k下,实部或虚部中所有的粘性曲线和理想曲线都相交于一点。这意味着在这些模式下,介电函数的实部或虚部跟切向粘滞无关。
我们应用粘性色流体方程计算的粘性介电函数,在线性响应近似下,计算了快速部分子在粘性QGP中运动时引起的尾迹势。通过介电函数,切向粘滞影响着尾迹势。数值结果表明,切向粘滞对尾迹势的影响跟快速部分子的运动速度相关系。v=0.99c时,相比于理想色流体力学的结果,粘滞效应使尾迹势的振荡行为变得更加显著。而当v=0.55c时,从数值结果上来看,切向粘滞对尾迹势的影响非常微小,所有的粘性势曲线同理想曲线都重叠在一起,所有的曲线间没有明显的差异。结合切向粘滞对介电函数的影响,以及介电函数对尾迹势的决定性作用,我们讨论解释了这种粘滞效应对尾迹势的速度相关的影响。
Quantum chromodynamics (QCD) predicts that deconfined phase transition will take place at high temperature and/or high density. As a result, the nuclear matter will undergo a transition to quark-gluon plasma (QGP) which is composed of quarks and gluons. Many theoretical studies indicate that the expected high temperature will reach by colliding two ultrarelativistic heavy nuclei at sufficiently high energy in laboratory. One main goal for the Relativistic Heavy Ion Collider (RHIC) is to seek this new state of matter. RHIC have provide several different colliding systems at a variety of energies and the vast data have been collected since its operation in 2000. Though there are controversies, many physicists argue that the QGP is produced at RHIC. However, it is not a long expected weak coupled QGP, but a strongly coupled and nearly perfect quark gluon fluid with a very small viscosity. To study global properties of the QGP is an urgent topic in heavy ion community. In this thesis, we focus on the color dielectric function of the QGP and the phenomena induced by a fast parton traveling through the QGP.
At first, we will briefly introduce some primary findings at RHIC, such as, elliptic flow v2, jet quenching and azimuthal dihadron correlation observable. Then, we will review foundations of finite temperature field theory, kinetic theory and hydrodynamics which are theoretical tools for the QGP.
With the hard thermal loop (HTL) resummation technique, we calculate the dielectric function excited by hard gluon in the quark-gluon plasma. We find that in the space-like regionω/k< 1, the real part of the dielectric function has two nontrivial extremum structures. At the same time, at theω/k where the extrema of the real part are located, the imaginary part of the dielectric function shows resonance structures. While the real and imaginary parts of dielectric function in the HTL approximation are both monotonously in the space-like region, showing no any resonance structures. These facts imply that properties of the dielectric function in the space-like region relate to some energy exchange mechanism—Landau damping. The main contributions of the resummation calculation come from the three and four gluon interactions which reflect nonlinear and non-Abelian nature of the quark-gluon plasma. Nonlinear and non-Abelian interaction will result in nonlinear Landau damping, which determines the properties of the dielectric function in the space-like region.
Within the framework of the linear response theory, by applying the dielectric function calcu- lated with the HTL resummation technique, we study the wake potential induced by a fast parton traveling through the QGP. In the backward direction, wake potential is a Lennard—Jones poten-tial at v= 0.55c, while the wake potential shows an obvious oscillatory behavior for v= 0.99c. In the forward direction, it is a modified Coulomb potential for both cases of v= 0.55c and v= 0.99c. In comparison with results calculated with the HTL dielectric function, nonlinear and non-abelian effects from the resummation calculation enhance anisotropy of the wake potential in the backward-forward directions. Finally, we give some explanations for those wake properties.
Viscosity will modify the distribution functions of quark and gluon. By using quark dis-tribution function modified by shear viscosity, we derive the viscous chromohydrodynamics by expanding the kinetic equation in momenta moments and truncating the expansion at the second moment level. In terms of the viscous chromohydrodynamic equations, we can derive the polar-ization tensor and the dielectric function. Whenη/s is small, such as the AdS/CFT bound 1/4π, the real part of the dielectric function deviates from the ideal chromohydrodynamic case (η/s= 0) slightly. With the increase ofη/s, its deviation becomes larger. Meanwhile, the imaginary part exhibits the similar properties. In addition, at some modes ofω/k, the real and the imaginary parts are independent on the shear viscosity. By analyzing the mathematical structures of the dielectric function, we give some explanations for the behavior.
By using the viscous dielectric function, we calculate the wake potential induced by a fast parton traveling through the viscous QGP. Through the dielectric function, shear viscosity af-fects the wake potential. The numerical analysis shows that viscous effects on wake potential are speed-dependent. In comparison with the ideal chromohydrodynamic results, shear viscosity make oscillation of wake potential more pronounced at v= 0.99c. While v= 0.55c, the viscous effects on the wake potential are so trivial in both the forward and backward directions and one can hardly distinguish all viscous potential curves from each other. Finally, we give some explanations for the speed-dependent viscous effects on the wake properties.
引文
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