强子—强子和相对论重离子碰撞中相空间的bin-bin多重数关联
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摘要
探索物质的质量起源和微观结构,是现代物理学研究的前沿领域。目前人们普遍认为夸克和胶子是物质的基本组成单元。量子色动力学(QCD)是描述夸克和胶子之间的强相互作用的一个成功的规范理论。QCD理论有两大基本特征,一是渐进自由,即当夸克之间的距离靠的很近时,耦合强度变得非常的小；二是夸克禁闭,即强相互作用具有长程的”色禁闭”特征,夸克被禁闭在强子内部,使得人们看不到自由的夸克。”夸克禁闭之谜”被称为20世纪物理学的一大疑云。20世纪七十年代,李政道等人提出：通过相对论重离子碰撞,有可能产生极大温度,极高密度的环境,形成解除禁闭的新物质形态——夸克胶子等离子体(QGP),从而在实验室里可以观察到自由的夸克和胶子。由此,相对论重离子碰撞的实验和理论研究迅速发展,称为跨世纪物理的一个重要方向。
本世纪伊始,美国布鲁克汶国家实验室(BNL)建立超高能的相对论重离子对撞机(RHIC),实现了平均每对核子200GeV的金金对撞。通过多年的努力,RHIC上发现了解禁闭的夸克胶子自由度,观察到了新物质相——夸克胶子等离子体。这一结论主要源于三个物理实验事实：1)在RHIC能区观察到形成新物质形态所需要的能量密度,它几乎是普通核物质能量密度的100倍；2)高横动量的粒子穿过热密物质时能有较大的能量损失；3)观测到末态粒子的各向异性集体流的行为,并且在中横动量区间,集体流具有组分夸克的标度性,这一物理性质能被理想流体力学模型很好的描述,因此人们称RHIC能区形成的新的物质为具有强耦合的夸克胶子等离子体,简称SQGP。
然而,理想流体力学模型描述各向异性椭圆流参数是存在一定的局限性,比如：仅限于描述低横动量区间粒子的椭圆流；不能很好的拟合不同粒子的椭圆流参数,尤其是重味粒子的情况；更有,200GeV质心能量下的铜铜碰撞的椭圆流的实验结果,远远大于理想流体力学计算的结果,几乎和相同碰撞能量下的金金碰撞具有相同的数量级。随后U.Heinz等人采用粘滞流体力学模型对这些实验结果进行重新拟合,通过调整模型中的粘滞系数,可以很好的重现这些物理实验数据。所有这些说明RHIC能区产生的新物质形态不是处于理想流体态,而是处于粘滞流体态。如何测量这种新物质形态的粘滞系数,成为大家关心的另一个热点问题。
本文建议利用相邻bin轴向角关联花样测量切向粘滞系数。理想流体中,层与层之间无相互作用,各流层的速度相同,没有速度梯度；粘质流体中,层与层之间存在相互作用,各流层的速度不同,有速度梯度。相邻bin轴向角关联花样能很好的描述这种流层与流层之间的相互作用,能反映集体流的内部相互作用信息。利用相邻bin轴向角关联花样与物质内部相互作用能的关系,结合粘滞流体力学耗散能的一些理论,本文给出了切向粘滞系数的具体计算公式。已知相对论重离子碰撞末态粒子的相关物理信息,就可以得到新物质形态的切向粘滞系数。因此,这种新的测量切向粘滞系数方法具有很强的可行性,为实验上研究新物质形态的性质提供了一种可能。
多相输运模型AMPT,既包含强子层次上的输运,又包括部分子层次上的输运,它是描述相对论重离子碰撞比较成功的唯象模型。本文以该模型为例,研究了RHIC能区的金金碰撞过程中形成的物质形态的粘滞系数。利用可记录的末态粒子的相关物理信息,我们给出了相邻bin关联花样和平均横向速度对轴向角的依赖关系。其中,平均横向速度采用的是热模型拟合的结果。作为一种比较,本文分别研究了散射截面为3mb和10mb的情况,结果发现,散射截面越大,对应的切向粘滞系数越小,这和目前微观理论计算的结果是相吻合的。
目前STAR测量的Forward-Backward关联的实验结果发现,快度方向上的长程关联会随着碰撞中心度的增大而逐渐增强,这和碰撞初态模型色玻璃凝聚预言的结果是相符的。由此,人们推测快度方向上的长程关联源于相对论重离子碰撞初态的色玻璃凝聚(CGC)效应,这对我们进一步的理解相对论重离子碰撞的时空演化图像,以及相关动力学机制有很大的帮助。然而,相关研究表明碰撞参数的起伏和短程关联的起伏也能引起快度方向上的长程关联。问题产生了,长程关联是一些统计起伏的结果,和CGC没有关系呢,还是主要是CGC的原因,统计起伏只是一个背景因素?
本文主要建议了两种快度关联花样——相邻bin快度关联花样和固定任意bin快度关联花样。这两种关联花样能同时记录关联强度随关联位置和关联长度的变化,是描述快度方向上的长短程关联很好的物理测量量。我们利用AMPT模型研究质心能量200GeV下金金碰撞的快度关联花样对碰撞中心度的依赖。随着中心度的增加,快度关联花样数值逐渐减小,对应的长程关联也在逐渐减弱,这和STAR测量Forward-Backward对中心度依赖的结果是不相符的。大家知道,在多相输运模型AMPT中,初始条件采用的是Glauber模型,而不是CGC模型。由此这可能间接说明相对论重离子碰撞的长程关联确实主要来自色玻璃凝聚(CGC)效应。另外,我们进一步研究了在弦融合AMPT模型产生固定碰撞参数事件样本中,快度关联花样和Forward-Backward关联对空间间隔的依赖。
在非中心碰撞中,椭圆流也能间接的描述碰撞初态的物理信息,是高能重离子碰撞中一个很重要的物理观测量。本文利用AMPT模型具体研究了固定碰撞参数下的椭圆流,比如椭圆流对参加者核子数的依赖,对末态多重数的依赖,随时间的演化规律等。结果发现,在不同的固定碰撞参数情况下,随着末态多重数的增加,椭圆流或单调增加,或单调减小,而不是大家预想中的仅仅只是个简单的起伏。随着系统的时空演化,椭圆流慢慢被建立起来,但是椭圆流并不总是在增加的。本文观测到椭圆流先增大而后有个减小的过程,我们推测是弦融合AMPT模型中的强子化机制——夸克融合模型,减弱了粒子产生过程中的各向异性行为。
Exploring the origin of matter and their microscopic structure is one of foreland fields of modern physics. It is generally considered today that quark and gluon are the component unit of matter. Quantum chromodynamics (QCD) is very successful to describe strong interaction between quark and gluon. The QCD theory has two basic properties. one is "asymptotic freedom". When quarks get very close, the coupling constant becomes extremely small. The other is "confined quark", that means quarks are confined in hadrons and there is no free quark. The mystery of quark confinement was thought as a great puzzle of the 20th century. In the 1970s, T.D.Lee et al. proposed that a new formed matter- Quark Gluon Plasma (QGP) would be produced in a environment with enough high density and high temperature, according the relativistic heavy ion collisions. This leads to the rapid development of cixperimental and theoretical study on relativistic heavy ion collision.
In the beginning of the century, the relativistic heavy ion collider (RHIC) was build and run in the Brookheaven National Laboratory in U.S. with colliding energy up to 200GeV/nucleon. Through several years of hard research, we observe parton (quark or gluon) degree of freedom and believe the new formed matter QGP has been formed. There are three major evidence:1)The energy density of initial state is nearly a hundred times greater than that of nuclear matter; 2)There are a large quantity of energy loss when particles at high pt go through the hot and dense matter; 3)The anisotropic collective behavior of particles has been observed and the elliptic flow of particles at medium pt has a property of quark scaling, all of which can be well described by ideal hydrodynamics. Combining these experimental results, we believe that the strongly coupled quark and gluon plasma has been formed(sQGP).
However, the ideal hydrodynamics model has some limitations on the description of elliptic flow. It can only describe the elliptic flow of particles at low pt region, but fail for that of high pt. It can't fit the elliptic flow parameter of different particles, especially the heavy flavor particles. What's more, for (?) GeV CuCu collision, the experimen-tal result of elliptic flow is much larger than the calculation of ideal hydrodynamics. Soon, U.heinz et al. applied the viscous hydrodynamics into the relativistic heavy ion collisions and prove it could well reproduce the experimental data through changing the viscosity parameter. All of these show the new formed matter is not ideal fluid, but viscous fluid. How to measure the viscosity of QGP becomes another key problem.
The neighboring azimuthal bin correlation pattern is suggested to measure the shear viscosity of the new matter. In ideal fluid, there is no internal interaction and the flow layer has the same viscosity. While in viscous fluid, internal interaction exists between layers and there is viscosity gradient. The new physicst measure can describe the interaction between fluid layers and reflect the internal information of collective flow. We derive the formula of shear viscosity by combing the dissipation energy theory in viscous hydrodynamics and the azimuthal correlation pattern. When the physics information of final particles is known, we can obtain the shear viscosity of new formed matter. In this view, the new method of measuring shear viscosity has a strong feasibility and can help us learn more about the new formed matter in current RHIC experiment.
A multi-phase transport model (AMPT) includes both hadron-level and parton-level interaction, which is a success to describe relativistic heavy ion collision. Based on this model, we explore the shear viscosity of dense matter produced in (?) GeV AuAu collision. We present the azimuthal angle dependence of neighboring bin correlation pat-tern and the average transverse velocity. The thermal model are used to fit the average transverse velocity of final particles. As a comparison, we study the case of cross sectionσ= 3mb andσ=10mb. It is found that the larger cross section is, the smaller the shear viscosity is, which is consistent with the calculation of microscopic theory.
In this paper, rapidity correlation pattern is also applied to relativistic heavy ion collision. Two correlation patterns-neighboring bin and fixed-to arbitrary rapidity correlation pattern are suggested. Different from the traditional physics measure of cor-relation, they can simultaneously record the change of correlation strength with spatial position of bin and the distance between bins. They can help us an excellent study of the short and long range correlation (LRC) in rapidity direction. In the market, forward-backward correlation from STAR experiment have inferred that the long range rapidity correlation pattern origins from the Color Glass Condensate (CGC) of initial state. How-ever, some research show that the fluctuation of multiplicity and short range correlation can also give rise to LRC. Is LRC a result of fluctuation or CGC?
We present the centrality dependence of rapidity correlation pattern for(?) GeV AuAu collision in the AMPT with string-melting. With the centrality increasing, it is observed that the value of correlation pattern decreases and the corresponding long range correlation is greatly weakened. This is not consistent with experimental data from This may indirectly prove the long range correlation is mainly from the effect of Color Glass Condensate. Moreover, in the samples for fixed impact parameter, we further study the rapidity gap dependence of correlation pattern and forward-backward correlation. It provides a way to eliminate or decrease at least the effect of fluctuation for LRC.
In non-central collision, elliptic flow is a key observable in the relativistic heavy ion collision, which can reflect the physics information of initial state. We study the multiplic-ity dependence of elliptic flow for Au+Au collisions at (?) GeV by AMPT with string melting. It is first shown that for at fixed impact factor b, elliptic flow varies with multiplicity monotonously but is not a simple fluctuation. After scaling elliptic flow by initial eccentricity of the nuclear overlap area, we obtain that it increases with centrality and then becomes a constant, which is indicated that the system has reached local ther-malization when the participant is large enough. Finally, we study the time evolution of elliptic flow and eccentricity. It is firstly observed that quark coalescence as hadronization scheme can reduce the momentum anisotropy of the system in the process of evolution.
本世纪伊始,美国布鲁克汶国家实验室(BNL)建立超高能的相对论重离子对撞机(RHIC),实现了平均每对核子200GeV的金金对撞。通过多年的努力,RHIC上发现了解禁闭的夸克胶子自由度,观察到了新物质相——夸克胶子等离子体。这一结论主要源于三个物理实验事实：1)在RHIC能区观察到形成新物质形态所需要的能量密度,它几乎是普通核物质能量密度的100倍；2)高横动量的粒子穿过热密物质时能有较大的能量损失；3)观测到末态粒子的各向异性集体流的行为,并且在中横动量区间,集体流具有组分夸克的标度性,这一物理性质能被理想流体力学模型很好的描述,因此人们称RHIC能区形成的新的物质为具有强耦合的夸克胶子等离子体,简称SQGP。
然而,理想流体力学模型描述各向异性椭圆流参数是存在一定的局限性,比如：仅限于描述低横动量区间粒子的椭圆流；不能很好的拟合不同粒子的椭圆流参数,尤其是重味粒子的情况；更有,200GeV质心能量下的铜铜碰撞的椭圆流的实验结果,远远大于理想流体力学计算的结果,几乎和相同碰撞能量下的金金碰撞具有相同的数量级。随后U.Heinz等人采用粘滞流体力学模型对这些实验结果进行重新拟合,通过调整模型中的粘滞系数,可以很好的重现这些物理实验数据。所有这些说明RHIC能区产生的新物质形态不是处于理想流体态,而是处于粘滞流体态。如何测量这种新物质形态的粘滞系数,成为大家关心的另一个热点问题。
本文建议利用相邻bin轴向角关联花样测量切向粘滞系数。理想流体中,层与层之间无相互作用,各流层的速度相同,没有速度梯度；粘质流体中,层与层之间存在相互作用,各流层的速度不同,有速度梯度。相邻bin轴向角关联花样能很好的描述这种流层与流层之间的相互作用,能反映集体流的内部相互作用信息。利用相邻bin轴向角关联花样与物质内部相互作用能的关系,结合粘滞流体力学耗散能的一些理论,本文给出了切向粘滞系数的具体计算公式。已知相对论重离子碰撞末态粒子的相关物理信息,就可以得到新物质形态的切向粘滞系数。因此,这种新的测量切向粘滞系数方法具有很强的可行性,为实验上研究新物质形态的性质提供了一种可能。
多相输运模型AMPT,既包含强子层次上的输运,又包括部分子层次上的输运,它是描述相对论重离子碰撞比较成功的唯象模型。本文以该模型为例,研究了RHIC能区的金金碰撞过程中形成的物质形态的粘滞系数。利用可记录的末态粒子的相关物理信息,我们给出了相邻bin关联花样和平均横向速度对轴向角的依赖关系。其中,平均横向速度采用的是热模型拟合的结果。作为一种比较,本文分别研究了散射截面为3mb和10mb的情况,结果发现,散射截面越大,对应的切向粘滞系数越小,这和目前微观理论计算的结果是相吻合的。
目前STAR测量的Forward-Backward关联的实验结果发现,快度方向上的长程关联会随着碰撞中心度的增大而逐渐增强,这和碰撞初态模型色玻璃凝聚预言的结果是相符的。由此,人们推测快度方向上的长程关联源于相对论重离子碰撞初态的色玻璃凝聚(CGC)效应,这对我们进一步的理解相对论重离子碰撞的时空演化图像,以及相关动力学机制有很大的帮助。然而,相关研究表明碰撞参数的起伏和短程关联的起伏也能引起快度方向上的长程关联。问题产生了,长程关联是一些统计起伏的结果,和CGC没有关系呢,还是主要是CGC的原因,统计起伏只是一个背景因素?
本文主要建议了两种快度关联花样——相邻bin快度关联花样和固定任意bin快度关联花样。这两种关联花样能同时记录关联强度随关联位置和关联长度的变化,是描述快度方向上的长短程关联很好的物理测量量。我们利用AMPT模型研究质心能量200GeV下金金碰撞的快度关联花样对碰撞中心度的依赖。随着中心度的增加,快度关联花样数值逐渐减小,对应的长程关联也在逐渐减弱,这和STAR测量Forward-Backward对中心度依赖的结果是不相符的。大家知道,在多相输运模型AMPT中,初始条件采用的是Glauber模型,而不是CGC模型。由此这可能间接说明相对论重离子碰撞的长程关联确实主要来自色玻璃凝聚(CGC)效应。另外,我们进一步研究了在弦融合AMPT模型产生固定碰撞参数事件样本中,快度关联花样和Forward-Backward关联对空间间隔的依赖。
在非中心碰撞中,椭圆流也能间接的描述碰撞初态的物理信息,是高能重离子碰撞中一个很重要的物理观测量。本文利用AMPT模型具体研究了固定碰撞参数下的椭圆流,比如椭圆流对参加者核子数的依赖,对末态多重数的依赖,随时间的演化规律等。结果发现,在不同的固定碰撞参数情况下,随着末态多重数的增加,椭圆流或单调增加,或单调减小,而不是大家预想中的仅仅只是个简单的起伏。随着系统的时空演化,椭圆流慢慢被建立起来,但是椭圆流并不总是在增加的。本文观测到椭圆流先增大而后有个减小的过程,我们推测是弦融合AMPT模型中的强子化机制——夸克融合模型,减弱了粒子产生过程中的各向异性行为。
Exploring the origin of matter and their microscopic structure is one of foreland fields of modern physics. It is generally considered today that quark and gluon are the component unit of matter. Quantum chromodynamics (QCD) is very successful to describe strong interaction between quark and gluon. The QCD theory has two basic properties. one is "asymptotic freedom". When quarks get very close, the coupling constant becomes extremely small. The other is "confined quark", that means quarks are confined in hadrons and there is no free quark. The mystery of quark confinement was thought as a great puzzle of the 20th century. In the 1970s, T.D.Lee et al. proposed that a new formed matter- Quark Gluon Plasma (QGP) would be produced in a environment with enough high density and high temperature, according the relativistic heavy ion collisions. This leads to the rapid development of cixperimental and theoretical study on relativistic heavy ion collision.
In the beginning of the century, the relativistic heavy ion collider (RHIC) was build and run in the Brookheaven National Laboratory in U.S. with colliding energy up to 200GeV/nucleon. Through several years of hard research, we observe parton (quark or gluon) degree of freedom and believe the new formed matter QGP has been formed. There are three major evidence:1)The energy density of initial state is nearly a hundred times greater than that of nuclear matter; 2)There are a large quantity of energy loss when particles at high pt go through the hot and dense matter; 3)The anisotropic collective behavior of particles has been observed and the elliptic flow of particles at medium pt has a property of quark scaling, all of which can be well described by ideal hydrodynamics. Combining these experimental results, we believe that the strongly coupled quark and gluon plasma has been formed(sQGP).
However, the ideal hydrodynamics model has some limitations on the description of elliptic flow. It can only describe the elliptic flow of particles at low pt region, but fail for that of high pt. It can't fit the elliptic flow parameter of different particles, especially the heavy flavor particles. What's more, for (?) GeV CuCu collision, the experimen-tal result of elliptic flow is much larger than the calculation of ideal hydrodynamics. Soon, U.heinz et al. applied the viscous hydrodynamics into the relativistic heavy ion collisions and prove it could well reproduce the experimental data through changing the viscosity parameter. All of these show the new formed matter is not ideal fluid, but viscous fluid. How to measure the viscosity of QGP becomes another key problem.
The neighboring azimuthal bin correlation pattern is suggested to measure the shear viscosity of the new matter. In ideal fluid, there is no internal interaction and the flow layer has the same viscosity. While in viscous fluid, internal interaction exists between layers and there is viscosity gradient. The new physicst measure can describe the interaction between fluid layers and reflect the internal information of collective flow. We derive the formula of shear viscosity by combing the dissipation energy theory in viscous hydrodynamics and the azimuthal correlation pattern. When the physics information of final particles is known, we can obtain the shear viscosity of new formed matter. In this view, the new method of measuring shear viscosity has a strong feasibility and can help us learn more about the new formed matter in current RHIC experiment.
A multi-phase transport model (AMPT) includes both hadron-level and parton-level interaction, which is a success to describe relativistic heavy ion collision. Based on this model, we explore the shear viscosity of dense matter produced in (?) GeV AuAu collision. We present the azimuthal angle dependence of neighboring bin correlation pat-tern and the average transverse velocity. The thermal model are used to fit the average transverse velocity of final particles. As a comparison, we study the case of cross sectionσ= 3mb andσ=10mb. It is found that the larger cross section is, the smaller the shear viscosity is, which is consistent with the calculation of microscopic theory.
In this paper, rapidity correlation pattern is also applied to relativistic heavy ion collision. Two correlation patterns-neighboring bin and fixed-to arbitrary rapidity correlation pattern are suggested. Different from the traditional physics measure of cor-relation, they can simultaneously record the change of correlation strength with spatial position of bin and the distance between bins. They can help us an excellent study of the short and long range correlation (LRC) in rapidity direction. In the market, forward-backward correlation from STAR experiment have inferred that the long range rapidity correlation pattern origins from the Color Glass Condensate (CGC) of initial state. How-ever, some research show that the fluctuation of multiplicity and short range correlation can also give rise to LRC. Is LRC a result of fluctuation or CGC?
We present the centrality dependence of rapidity correlation pattern for(?) GeV AuAu collision in the AMPT with string-melting. With the centrality increasing, it is observed that the value of correlation pattern decreases and the corresponding long range correlation is greatly weakened. This is not consistent with experimental data from This may indirectly prove the long range correlation is mainly from the effect of Color Glass Condensate. Moreover, in the samples for fixed impact parameter, we further study the rapidity gap dependence of correlation pattern and forward-backward correlation. It provides a way to eliminate or decrease at least the effect of fluctuation for LRC.
In non-central collision, elliptic flow is a key observable in the relativistic heavy ion collision, which can reflect the physics information of initial state. We study the multiplic-ity dependence of elliptic flow for Au+Au collisions at (?) GeV by AMPT with string melting. It is first shown that for at fixed impact factor b, elliptic flow varies with multiplicity monotonously but is not a simple fluctuation. After scaling elliptic flow by initial eccentricity of the nuclear overlap area, we obtain that it increases with centrality and then becomes a constant, which is indicated that the system has reached local ther-malization when the participant is large enough. Finally, we study the time evolution of elliptic flow and eccentricity. It is firstly observed that quark coalescence as hadronization scheme can reduce the momentum anisotropy of the system in the process of evolution.
引文
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[26]Z. W. Lin, C. M. Ko and S. Pal, Phys. Rev. Lett.89,152301 (2002).
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[28]Z.W.Lin and C.M.Ko, Phys.ReV.C65,034904(2002).
[29]Z.W.Lin, C.M.Ko and S.Pal, Phys.ReV.Lett.89,152301(2002).
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[39]J.Adams et al(STAR Collabration), Nucl.Phys.A757,102(2005).
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[42]G. Policastro, D. T. Son and A.O. Starinets, Phys. Rev. Lett.87,081601 (2001).
[43]P. Arnold, G. D. Moore and L. G. Yaffe, JHEP 0011,001 (2000),JHEP 0305,051 (2003).
[44]H. B. Meyer, Phys. Rev. D 76,101701 (2007).
[45]S. Gavin and M. Abdel-Aziz, Phys. Rev. Lett.97,162302 (2006).
[46]M. Luzum and P. Romatschke, Phys. Rev. C 78,034915 (2008).
[47]H. Song and U. W. Heinz, arXiv:0812.4274 [nucl-th].
[48]A.K.Chandhuri, arXiv:0909.0391v1.
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[51]K.Dusling and D.Teaney, Phys.Rev.C77,034905(2008).
[52]B.Alver et al.(PHOBOS Collabration), arXiv:nucl-ex/0702036v1.
[53]J.Adams et al.(STAR Collabration), Phys.Rev.Lett92,062301(2004).
[54]Wang Meijuan, Liu Lianshou, Wu Yuanfang, CPC (HEP&NP), Vol33,1(2009).
[55]B. Alver, et al., arXiv:0711.3724.ib
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[64]Brijesh K.Srivastava, Int.J.Mod.Phys.E16,3371-3378(2008).
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[66]A. Capella et al., Phys. Rep.236,225 (1994).
[67]N. Armesto, L. McLerran and C. Pajares, Nucl. Phys. A781,201 (2007).
[68]M. Abdel-Aziz, and M. Bleicher, nucl-th/0605072.
[69]B. B. Back et al., Phys. Rev. Lett.91,052303 (2003).
[70]高能碰撞多粒子产生,刘连寿,吴元芳著,上海科学出版社,1998年12月.
[71]B.B.Back et al.(PHOBOS Collaboration), Phys. Rev. C74,011901(2006).
[72]K. Alpgard et al. [UA5 Collaboration], Phys. Lett. B 123,361 (1983).
[73]L. J. Shi and S. Jeon, Phys. Rev. C 72,034904 (2005).
[74]B.I.Abelev et al.(STAR Collaboration), Phys. Rev. Lett.103,172301(2009).
[75]S.Voloshin and Y.Zhang, Z.Phys.C70,665(1996).
[76]B.Alessandro et al(ALICE Collaboration), J.Phys.G:Nucl. Part. Phys.32, 1295(2006).
[77]H. Stocker et al, Phys. Rev., C25,1873(1982); H. H. Gutbrod et al., Phys. Lett. B216,267(1989).
[78]Jean-Yves Ollitrault, Nucl. Phys. A638,195-206(1998); P. Danielewicz, Nucl. Phys. A685,368-383(2001).
[79]H. Liu, S. Panitkin, and N. Xu, Phys. Rev. C59,348(1999).
[80]P. Huovinen, P.F. Kolb, U. Heinz, P.V. Ruuskanen and S.A. Voloshin, Phys. Lett. B 503,58 (2001).
[81]J. Adams et al. (STAR Collab.), Phys. Rev. Lett.92,052302 (2004).
[82]J. Castillo et al. (STAR Collab.), J. Phys. G 30, S1207 (2004).
[83]S.S. Adler et al. (PHENIX Collab.), Phys. Rev. Lett.91,182301 (2003).
[84]S.A. Voloshin, Nucl. Phys. A 715,379c (2003); D. Molnar and S.A. Voloshin, Phys. Rev. Lett.91,092301 (2003); R.J. Fries, B. Miiller, C. Nonaka and S.A. Bass, Phys. Rev. Lett.90,202303 (2003); V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett.90,202302 (2003); C. Nonaka, R.J. Fries and S.A. Bass, Phys. Lett. B 583,73 (2004); C. Nonaka et al., Phys. Rev. C 69,031902(2004).
[85]Hirano T, Acta Phys Polon B36,187(2005); Ulrich W.Heinz, nucl-th/05012051, proceeding for "Extreme QCD".
[86]Rachid Nouiccr et al(PHOBOS Collabration), J.Phys.G34, S887(2007).
[87]Michanel L.Miller, Klaus Reygers, Stephen J.Sanders and Peter Steinberg, Ann.Rev.Nucl.Part.Sci57,205-243(2007).
[88]Kharzcev D and Nardi M, Phys.Lett.B507,121(2001).
[89]B.Alvcr et al.(PHOBOS),Phys.Rev.Lett.98,242302(2007).
[90]H.Appelshauscr et al.(NA49 Collaboration), Phys.Rev.Lett.80,4136(1998).
[91]P.F.Kolb, J.Sollfrank and U.Heinz, Phys.Lett.B459,667(1999).
[92]Peter F.Kolb, Josef Sollfrank and Ulrich Heinz, Phys.Rev.C62,054909(2000).
[93]H. J. Drescher, A. Dumitru, C. Gombeaud and J. Y. Ollitrault, Phys.ReV.C76, 024905(2007).
[94]B.I. Abelev et al. (STAR Collaboration), Phys. Rev. Lett.99,112301 (2007).
[95]P. Huovinen and P.V. Ruuskanen, Ann. Rev. Nucl. Part. Sci.56,163 (2006).