130GeV金-金核碰撞中K_S～O和∧+？的方位角各向异性和强子-强子碰撞中单事件阶乘矩的随机性行为
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摘要
几千年来，人类一直探索什么是物质的最终组成部分?最近几百年的科技发展使我们对这一问题的认识不断深入。原子可以再分为电子和原子核。原子核又是由核子通过强相互作用而结合在一起的。强相互作用的基本理论，量子色动力学(QCD)，指出所有参与强相互作用的基本粒子都是夸克(q)及反夸克((?))的束缚态。到目前为止，没有观察到自由存在的夸克，但它们参与强相互作用并形成三夸克的重子或是夸克反夸克结合成为介子。QCD预测在极高的能量密度下，强子物质会解除禁闭而成为夸克胶子的等离子态。1986/1987年，在美国布鲁海汶国家实验室与欧洲的核子研究中心先后开始了固定靶实验的高能核-核碰撞，从各方面对高密度下的核物质进行了大量的研究。2000年夏天，新的相对论重离子对撞机(RHIC)在美国布鲁海汶国家实验室投入运行，其质心能量大约是以往固定靶实验的7.5倍。五年以后的大型强子对撞机将在更高的能量下实现核-核对撞。
相对论重粒子碰撞将产生能量密度远高于正常核物质的强相互作用物质。我们将研究物质在极端温度、压强和能量密度下的行为。夸克由于受到相互作用势V_0(Υ)～σΥ而被束缚于强子中。在极高的能量密度下，类似于量子电动力学(QED)中的“德拜屏蔽”，夸克胶子间的相互作用有可能不再随距离的增大而趋于无穷大，这使夸克胶子可以超出强子，在较大的范围内运动，形成夸克-胶子等离子体(QGP)。格点QCD预言了这一由强子物质到夸克-胶子等离子体相变的存在。相对论热动力学指出，高密度可以通过增加系统的净重子数密度或对系统“加热”来实现。不同碰撞能量下的实验将使我们可以探测系统在不同能量与净重子数密度下的行为。
目前的RHIC实验正在研究质心系能量200GeV每核子的金核对撞。在RHIC能区上，大部分入射核中的核子都会被入射核带走而在碰撞的中心区以夸克胶子的形式留下大量的能量，形成一个高能量密度、低净重子数的碰撞区。这将与早期宇宙的条件十分类似。
相对论重离子碰撞过程可以简单地概括为两个高度洛仑兹收缩的核以接近光速对撞并在对撞区内产生大量的夸克与胶子。夸克胶子相互作用并在一定的时候强子化，产生的强子进一步相互作用并最终停止相互作用成为末态观察到的强
f艺回r＼博士学位论文
M DOCI”OR．AL DISSERTAI”ION
子。到目前为止，还没有一个完整的动力学理论可以解释核－核碰撞的所有基本
过程。量子色动力学只有在高动量下，可以运用微扰方法时，才是可以计算的。
在RHIC能量下，大量产生的微喷注使我们第一次可以通过微扰QCD来研究核－核
碰撞。在较低的AGS和SPS能量上一般采用的方法是通过合适的动力学模型拟合＿
末态观察量。这其中，最重要的就是相对论流体力学。其基本假设是系统达到了
局域的热平衡和化学平衡。尽管仍存在一些理论上的问题，理想流体力学的结果 甲
能很好地符合RHIC在低动量范围内的实验结果。
不同于基本的强于－强子碰撞，核－核碰撞中会有大量的核了相互作用，并产生
一些“集体行为”。这里“集体行为”指在一次碰撞中所观察到的多个粒子的共
同性质。我们通常称这种大量产生的粒子具有相似的运动方向和速度为“集体
流”。将集体流用运动学变量来表示，我们得到各种类型的流。“纵向流”：描
述粒子在初始束流方向上的集体运动；“径向流”：描述产生的粒子具有相似的
与方向无关的速度，即速度场具有球对称性；“横向流”：描述速度场与方位角
无关；“各向异性流”：描述粒子产生在某一方位角的方向上会大于其它方向。
各种形式的流都是相互联系的，它们代表了核－核碰撞整体图像的不同方面。这篇
论文中所讨论的椭球流属于各向异性流。
我们称碰撞参数b＝0的碰撞为对心碰撞。这类碰撞具有初始的方位角对称
性。而在实验中大量存在的是b＞0的非对心碰撞。这类碰撞不具有初始的方位角
对称性。对于这类事件，我们应相对于它们初始的方位角不对称的方向来研究它
们，而这一方向由它们各自碰撞参数的取向和大小完全决定。我们定义由碰撞参
数矢量和束流动量方向所诀定的平面为“反应平面”。在非对心碰撞中，初始坐
标空间中的方位角不对称性将导致末态粒子相对于“反应平面”的角依赖性。微
观上讲，末态动量空间的大的各向异性来源于碰撞最初阶段的大量的再散射。从
流体力学的角度上讲，横向平面上的压强差诀定了系统的演化。在初始椭球的短
轴方向上会产生较大的压强差，而使更多的粒子向这一方向上运动并逐步减小长
短轴方向上的差别。由此可见，末态所观察到的各向异性来源于碰撞的早期。我
们定义各向异性流为粒子相对于反应平面分布的不对称性并通常用方位角分布的
傅立叶变换来描述这一不对称性。由于方位角分布中不为零的第二谐波系数对应
于椭圆，我们称第二谐波项为“椭球流”。它描述了反应平面方向与垂直于反应
平面方向各向异性的粒于发射。到目前为止，对于各向异性流的测量大多只限于
n
— —
非奇异粒子，只有少数低能实?
The operation and first collisions of Au nuclei in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) during year 2000 began a new era in the study of nuclear matter at high energy density and the search of Quark-Gluon Plasma (QGP). The properties of the QGP and the transition to it have to be identified from the final state which is of a hadronic nature. Measurements of azimuthal anisotropies in the transverse momentum distribution of particles can probe the very early stages of ultra-relativistic heavy-ion collisions. This dissertation presents the STAR results on the azimuthal anisotropy parameter v-i for strange particles K^, A arid A at mid-rapidity in Au+Au collisions at ^/SNN = 130 GeV at RHIC. The value of w2 as a function of transverse momentum pt and collision centrality is presented for both particles up to ~ 3.0 GeV/c. A strong pt dependence in u2 is observed up to 2.0 GeV/c. The w2 measurement is compared with hydrodynamic model calculations. The physics implication of the pt integrated v% magnitude as a function of particle mass is also discussed.
Erraticity analysis provide new opportunity in measuring event by event fluctuations in high energy nuclear collisions. In the second part of this dissertation (chapter 6 and chapter 7), it is demonstrated that in low multiplicity sample, the increase of the fluctuation of event factorial moments with the diminishing of phase space scale, "erraticity", are dominated by the statistical fluctuations. Applying erraticity analysis to high multiplicity sample at RHIC and LHC energy is recommended.
相对论重粒子碰撞将产生能量密度远高于正常核物质的强相互作用物质。我们将研究物质在极端温度、压强和能量密度下的行为。夸克由于受到相互作用势V_0(Υ)～σΥ而被束缚于强子中。在极高的能量密度下，类似于量子电动力学(QED)中的“德拜屏蔽”，夸克胶子间的相互作用有可能不再随距离的增大而趋于无穷大，这使夸克胶子可以超出强子，在较大的范围内运动，形成夸克-胶子等离子体(QGP)。格点QCD预言了这一由强子物质到夸克-胶子等离子体相变的存在。相对论热动力学指出，高密度可以通过增加系统的净重子数密度或对系统“加热”来实现。不同碰撞能量下的实验将使我们可以探测系统在不同能量与净重子数密度下的行为。
目前的RHIC实验正在研究质心系能量200GeV每核子的金核对撞。在RHIC能区上，大部分入射核中的核子都会被入射核带走而在碰撞的中心区以夸克胶子的形式留下大量的能量，形成一个高能量密度、低净重子数的碰撞区。这将与早期宇宙的条件十分类似。
相对论重离子碰撞过程可以简单地概括为两个高度洛仑兹收缩的核以接近光速对撞并在对撞区内产生大量的夸克与胶子。夸克胶子相互作用并在一定的时候强子化，产生的强子进一步相互作用并最终停止相互作用成为末态观察到的强
f艺回r＼博士学位论文
M DOCI”OR．AL DISSERTAI”ION
子。到目前为止，还没有一个完整的动力学理论可以解释核－核碰撞的所有基本
过程。量子色动力学只有在高动量下，可以运用微扰方法时，才是可以计算的。
在RHIC能量下，大量产生的微喷注使我们第一次可以通过微扰QCD来研究核－核
碰撞。在较低的AGS和SPS能量上一般采用的方法是通过合适的动力学模型拟合＿
末态观察量。这其中，最重要的就是相对论流体力学。其基本假设是系统达到了
局域的热平衡和化学平衡。尽管仍存在一些理论上的问题，理想流体力学的结果 甲
能很好地符合RHIC在低动量范围内的实验结果。
不同于基本的强于－强子碰撞，核－核碰撞中会有大量的核了相互作用，并产生
一些“集体行为”。这里“集体行为”指在一次碰撞中所观察到的多个粒子的共
同性质。我们通常称这种大量产生的粒子具有相似的运动方向和速度为“集体
流”。将集体流用运动学变量来表示，我们得到各种类型的流。“纵向流”：描
述粒子在初始束流方向上的集体运动；“径向流”：描述产生的粒子具有相似的
与方向无关的速度，即速度场具有球对称性；“横向流”：描述速度场与方位角
无关；“各向异性流”：描述粒子产生在某一方位角的方向上会大于其它方向。
各种形式的流都是相互联系的，它们代表了核－核碰撞整体图像的不同方面。这篇
论文中所讨论的椭球流属于各向异性流。
我们称碰撞参数b＝0的碰撞为对心碰撞。这类碰撞具有初始的方位角对称
性。而在实验中大量存在的是b＞0的非对心碰撞。这类碰撞不具有初始的方位角
对称性。对于这类事件，我们应相对于它们初始的方位角不对称的方向来研究它
们，而这一方向由它们各自碰撞参数的取向和大小完全决定。我们定义由碰撞参
数矢量和束流动量方向所诀定的平面为“反应平面”。在非对心碰撞中，初始坐
标空间中的方位角不对称性将导致末态粒子相对于“反应平面”的角依赖性。微
观上讲，末态动量空间的大的各向异性来源于碰撞最初阶段的大量的再散射。从
流体力学的角度上讲，横向平面上的压强差诀定了系统的演化。在初始椭球的短
轴方向上会产生较大的压强差，而使更多的粒子向这一方向上运动并逐步减小长
短轴方向上的差别。由此可见，末态所观察到的各向异性来源于碰撞的早期。我
们定义各向异性流为粒子相对于反应平面分布的不对称性并通常用方位角分布的
傅立叶变换来描述这一不对称性。由于方位角分布中不为零的第二谐波系数对应
于椭圆，我们称第二谐波项为“椭球流”。它描述了反应平面方向与垂直于反应
平面方向各向异性的粒于发射。到目前为止，对于各向异性流的测量大多只限于
n
— —
非奇异粒子，只有少数低能实?
The operation and first collisions of Au nuclei in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) during year 2000 began a new era in the study of nuclear matter at high energy density and the search of Quark-Gluon Plasma (QGP). The properties of the QGP and the transition to it have to be identified from the final state which is of a hadronic nature. Measurements of azimuthal anisotropies in the transverse momentum distribution of particles can probe the very early stages of ultra-relativistic heavy-ion collisions. This dissertation presents the STAR results on the azimuthal anisotropy parameter v-i for strange particles K^, A arid A at mid-rapidity in Au+Au collisions at ^/SNN = 130 GeV at RHIC. The value of w2 as a function of transverse momentum pt and collision centrality is presented for both particles up to ~ 3.0 GeV/c. A strong pt dependence in u2 is observed up to 2.0 GeV/c. The w2 measurement is compared with hydrodynamic model calculations. The physics implication of the pt integrated v% magnitude as a function of particle mass is also discussed.
Erraticity analysis provide new opportunity in measuring event by event fluctuations in high energy nuclear collisions. In the second part of this dissertation (chapter 6 and chapter 7), it is demonstrated that in low multiplicity sample, the increase of the fluctuation of event factorial moments with the diminishing of phase space scale, "erraticity", are dominated by the statistical fluctuations. Applying erraticity analysis to high multiplicity sample at RHIC and LHC energy is recommended.
引文
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