相对论重离子碰撞中的相变动力学和神经网络在粒子鉴别中的应用
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摘要
强相互作用的基本理论量子色动力学(QCD)有微扰真空和物理真空两种不同的真空态，带色的夸克和胶子不能在通常的物理真空中运动，而只能被禁闭在色中性的强子中。QCD真空的这种复杂结构被李政道称为“看不见的夸克”，是跨世纪物理学的“两大困惑”之一。上世纪70年代末，李政道等人预言：高能核-核碰撞能改变真空的性质，产生在大范围内解除禁闭的夸克胶子系统—夸克胶子等离子体(Quark Gluon Plasma)，推动了相对论重离子碰撞的理论和实验研究，形成跨世纪物理学的一个主流。进入新世纪，相对论重离子对撞机RHIC在美国布鲁克海汶国家实验室建成运行，碰撞能标达到千亿电子伏，发现了大量新实验现象。已经观察到在比强子体积大千倍的范围内出现的部分子(夸克和胶子)自由度。这意味着在此范围内色禁闭被解除，QCD真空发生改变。进一步深入研究这种解除了禁闭的夸克胶子系统的性质，特别是它和通常强子系统之间的转变，即：QCD的微扰真空和物理真空之间的转变，是当前乃至今后物理学最重要的研究课题之一。
格点规范理论给出的QCD相图是：在低温高密区，QGP和通常强子物质之间是一级相变；随着温度的升高和重子数密度的降低，相变曲线在临界点终止；在更高温度和更低密度下，QGP和通常的强子物质之间平滑过渡(cross over)。
在目前的相对论重离子碰撞实验中，虽然已经观察到解除禁闭的夸克-胶子自由度，但还未能看到它和强子物质之间的转变过程，特别是没有能找到临界点和在临界点之下的一级相变。RHIC实验正在调低碰撞能量，进行能量扫描，希望找到临界点。德国核物理研究所GSI也在建造新的强流环来研究低温时的相变。
对于相对论重离子碰撞的时空演化，常常采用输运模型做蒙特卡罗模拟研究。输运模型是输运方程的数值解。它通过输入核几何和反应截面来追踪碰撞的过程。相对论重离子碰撞的多相输运模型AMPT中包含有部分子相和强子相，比较适合于研究两相之间的转变。这一模型在给定散射截面后，让每个部分子一直演化下去，直到它和其它部分子的相互作用停止为止。这种办法使得部分子到强子之间的转变成为单个部分子的个体行为，而不是整个系统的集体行为。每个部分子有自己的强子化时间，而整个部分子系统没有统一的强子化时间。这样，部分子相和强子相之间如何转化(相变或平滑过渡)的问题被回避了。而由此就出现了在绝大多数部分子都已强子化，系统已回到物理真空后，还有少数部分子在强子系统(物理真空)中自由运动的不合理情况。
为了解决输运模型中存在的这一问题，必须考虑如何在现有的输运模型中实现相变的物理过程。在这篇论文中，我们以相对论重离子碰撞的两相输运模型为例，研究了模型中各个物理量的时间演化。在假设系统达到局域热平衡的条件下，我们采用考虑了流效应的热模型，拟合各个时刻粒子不变横质量分布，得到部分子和强子系统在各个时刻的温度。根据部分子和强子温度随时间的变化，我们引入包含过冷态的相变的物理图像，要求输运模型中所有部分子在达到过冷后发生突然相变，一起强子化。在模型中加入包含过冷态的相变后，我们发现，与原始模型相比，有相变的模型不仅保持了原始模型很好地符合椭圆流强度的实验数据的优点，同时还能更好地描述末态带电粒子的纵向快度分布。我们的尝试说明，为了更好地描述相对论重离子碰撞的过程，在重离子碰撞的输运模型中引入对相变动力学的模拟是非常有必要的。
在粒子物理实验中，如何更准确地鉴别粒子一直是非常重要的问题。在当前的重离子碰撞实验中，提高奇异重子Ξ和Ω的鉴别效率对它们的椭圆流的测量精度有重要影响，同时也能为实验上发现的夸克胶子自由度给出更确凿的证据。理论预言在重离子碰撞所形成的夸克胶子等离子体的环境下极有可能生成由六个奇异夸克组成的(ΩΩ)反常态。为了找到这类产额很小粒子，有必要研究更有效的粒子鉴别方法。
人工神经网络方法是一种模拟人脑神经系统的具有非线性动力学特征的信息处理系统，在模式识别、自动控制、图象处理等领域有着广泛的应用。90年代初期，神经网络方法被用到高能物理实验中处理径迹重建、能量团重建和粒子识别等问题并展示了一定的优越性。在这篇论文中，我们将研究利用神经网络如何提高粒子鉴别效率。首先我们利用神经网络来识别蒙特卡罗产生的正负电子在91.2GeV碰撞下生成的夸克喷注和胶子喷注，考察了一些影响神经网络判别性能的因素，以获得关于应用神经网络的一些规律性的知识。然后神经网络方法被用来重建RHIC上的STAR探测器收集到的氘核-金核在(s_(NN))~(1／2)=200GeV碰撞下的数据中的Λ粒子。神经网络方法重建Λ粒子的效率比参量截断法高29％，但信噪比比参量截断法低。最后我们讨论了将自适应增强算法应用于神经网络，提高神经网络性能的可能性。我们考虑了两种样本集，第一种是信号和背景可分但两者边界不规则的简单二维模型，第二种是信号和背景间有重叠的蒙特卡罗夸克胶子喷注。我们发现增强法能提高第一种样本集的判别效率和信噪比，但不能改善第二种样本集的判别性能。
The theory of Quantum Chromo-Dynamics, which describes the strong interactions, has two different vacuum states—perturbative vacuum and physical vacuum. Colored quarks and gluons can only exist in physical vacuum and are confined in color neutral hadrons. In 1970s, T.D. Lee et al. predicted that a new state of matter—quark gluon plasma will be formed while the phase transition from physical vacuum to perturbative vacuum happens in high energy nucleus-nucleus collisions. Since then, great progress has been made in the experimental and theoretical fields of heavy ion collisions. In the new century, the relativistic heavy ion collider(RHIC) in the Brookheaven National Laboratory in U.S. with colliding energy above several hundred GeV has started taking data and obtained a lot of new results. Combining all of the experimental results, people believe that partonic(quark and gluon) degree of freedom has been formed in the volume about thousands times that of hadrons. It means that the color confinement of quarks has disappeared and the transition between physical vacuum and perturbative vacuum happened. What's the character of the formed new state of de-confined quark and gluon? How to transfer from normal hadron to de-confined quarks and gluons? These will be the most important research topics in the present and future physics.
The QCD phase diagram predicted by lattice gauge theory is the following: in the region with high baryon density and low temperature the transition between normal hadron matter and QGP is a first order phase transition. As the increase of temperature and decrease of baryon density, the line of the first order phase transition ends at the critical point and in higher temperature and lower density region, there is a cross-over from normal hadron to QGP.
From the current experimental results, people has not found the critical point and the first order phase transition below critical point. In order to study the phase transition, RHIC will run at lower beam energies and GSI in Germany is building new facilities to satisfy the low temperature and high baryon density condition.
Transport models are usually used to study the time and space evolution of heavy ion collisions. The transport model, which is a numerical solution of transport equation, will follow the collision process by inputting the nuclear geometry and reaction cross-section. The multiphase transport model of heavy ion collision includes parton phase and hadron phase and is suitable for the study of phase transition. In this model the partons are allowed to transport until ceasing interactions with other partons at given scattering cross section. By this means the transition between partons and hadrons is a parton-wise behavior instead of a collective one, resulting in individual hadronization time of partons. It's unreasonable that a few partons move freely in a system full of hadrons after most of the partons has already hadronize to hadrons and the perturbative vacuum turned to physical one.
To solve this problem, we need to consider how to realize collective phase transition in transport model. In this thesis, taken the AMPT model as example, we investigate the time evolution of some physical quantities in the model. Assume the system achieves local thermal equilibrium, the temperature of partons and hadrons are extracted respectively by fitting their invariant transverse mass distribution to a thermal + radial flow model. Based on the parton and hadron temperature evolution, we implement a collective sudden phase transition following a supercooling state to the model by requiring all partons hadronize at the same time after the supercooling state. It turns out that the modified model with a sudden phase transition inherits the success of the original one in elliptic flow and is able to reproduce the experimental longitudinal distributions of final state particles better than the original one does. The encouraging results indicate that equilibrium phase transition should be taken into proper account in parton transport models for relativistic heavy ion collisions.
Particle identification is important in experimental physics. In the current heavy ion collisions, higher reconstruction efficiency of strange baryons likeΞandΩis crucial to the precise measurement of elliptic flow and to the confirmation of the discovery of parton degree of freedom. Theorists have predicted that extotic multi-quark state (ΩΩ) of six strange quarks could be formed in quark gluon plasma. In order to find this kind of low yield particles, more efficient particle identification methods are called for.
Artificial neural network is a kind of information processor with nonlinear dynamical properties by simulating the neuron system of human brain. It had been widely used in the fields such as pattern recognition, auto control, image process. In the early 1990s, neural network method was introduced to high energy experimental physics and it is found to be promising in dealing with the problem as track reconstruction, energy cluster reconstruction and particle identification. In this thesis, we will study how to improve the particle identification efficiency by using neural network method. At first, the neural network is applied to quark and gluon jets produced from the Monte Carlo simulation of e~+e~- collision at s~(1/2) = 91.2GeV. From this application, some factors which will affect the performance of neural network are investigated. Then neural network is used to reconstruct the A particles from (sNN)~(1/2) = 200GeV d-Au collision data taken by RHIC STAR detector. Comparing track-cutting method with neural network, we found that the reconstruction efficiency of A particles by neural network method is 29% higher than that of the cutting method, but the signal-background ratio of the reconstruction by neural network method is lower than that of the cutting method. In order to improve the performance of neural network, a kind of re-sampling technique—adaptive boosting algorithm, is combined with neural network. To study the classification ability of boosted neural network, two different cases are considered, one is the two dimensional toy model in which signal and background are separable with irregular boundaries, the other is the Monte Carlo quark and gluon jets samples in which signal and background are overlapped with each other. We found that the boosting technique is able to improve the classification efficiency and signal-background ratio in the first case, i.e. the separable samples, but failed for the second case where there are mixing between signal and background.
格点规范理论给出的QCD相图是：在低温高密区，QGP和通常强子物质之间是一级相变；随着温度的升高和重子数密度的降低，相变曲线在临界点终止；在更高温度和更低密度下，QGP和通常的强子物质之间平滑过渡(cross over)。
在目前的相对论重离子碰撞实验中，虽然已经观察到解除禁闭的夸克-胶子自由度，但还未能看到它和强子物质之间的转变过程，特别是没有能找到临界点和在临界点之下的一级相变。RHIC实验正在调低碰撞能量，进行能量扫描，希望找到临界点。德国核物理研究所GSI也在建造新的强流环来研究低温时的相变。
对于相对论重离子碰撞的时空演化，常常采用输运模型做蒙特卡罗模拟研究。输运模型是输运方程的数值解。它通过输入核几何和反应截面来追踪碰撞的过程。相对论重离子碰撞的多相输运模型AMPT中包含有部分子相和强子相，比较适合于研究两相之间的转变。这一模型在给定散射截面后，让每个部分子一直演化下去，直到它和其它部分子的相互作用停止为止。这种办法使得部分子到强子之间的转变成为单个部分子的个体行为，而不是整个系统的集体行为。每个部分子有自己的强子化时间，而整个部分子系统没有统一的强子化时间。这样，部分子相和强子相之间如何转化(相变或平滑过渡)的问题被回避了。而由此就出现了在绝大多数部分子都已强子化，系统已回到物理真空后，还有少数部分子在强子系统(物理真空)中自由运动的不合理情况。
为了解决输运模型中存在的这一问题，必须考虑如何在现有的输运模型中实现相变的物理过程。在这篇论文中，我们以相对论重离子碰撞的两相输运模型为例，研究了模型中各个物理量的时间演化。在假设系统达到局域热平衡的条件下，我们采用考虑了流效应的热模型，拟合各个时刻粒子不变横质量分布，得到部分子和强子系统在各个时刻的温度。根据部分子和强子温度随时间的变化，我们引入包含过冷态的相变的物理图像，要求输运模型中所有部分子在达到过冷后发生突然相变，一起强子化。在模型中加入包含过冷态的相变后，我们发现，与原始模型相比，有相变的模型不仅保持了原始模型很好地符合椭圆流强度的实验数据的优点，同时还能更好地描述末态带电粒子的纵向快度分布。我们的尝试说明，为了更好地描述相对论重离子碰撞的过程，在重离子碰撞的输运模型中引入对相变动力学的模拟是非常有必要的。
在粒子物理实验中，如何更准确地鉴别粒子一直是非常重要的问题。在当前的重离子碰撞实验中，提高奇异重子Ξ和Ω的鉴别效率对它们的椭圆流的测量精度有重要影响，同时也能为实验上发现的夸克胶子自由度给出更确凿的证据。理论预言在重离子碰撞所形成的夸克胶子等离子体的环境下极有可能生成由六个奇异夸克组成的(ΩΩ)反常态。为了找到这类产额很小粒子，有必要研究更有效的粒子鉴别方法。
人工神经网络方法是一种模拟人脑神经系统的具有非线性动力学特征的信息处理系统，在模式识别、自动控制、图象处理等领域有着广泛的应用。90年代初期，神经网络方法被用到高能物理实验中处理径迹重建、能量团重建和粒子识别等问题并展示了一定的优越性。在这篇论文中，我们将研究利用神经网络如何提高粒子鉴别效率。首先我们利用神经网络来识别蒙特卡罗产生的正负电子在91.2GeV碰撞下生成的夸克喷注和胶子喷注，考察了一些影响神经网络判别性能的因素，以获得关于应用神经网络的一些规律性的知识。然后神经网络方法被用来重建RHIC上的STAR探测器收集到的氘核-金核在(s_(NN))~(1／2)=200GeV碰撞下的数据中的Λ粒子。神经网络方法重建Λ粒子的效率比参量截断法高29％，但信噪比比参量截断法低。最后我们讨论了将自适应增强算法应用于神经网络，提高神经网络性能的可能性。我们考虑了两种样本集，第一种是信号和背景可分但两者边界不规则的简单二维模型，第二种是信号和背景间有重叠的蒙特卡罗夸克胶子喷注。我们发现增强法能提高第一种样本集的判别效率和信噪比，但不能改善第二种样本集的判别性能。
The theory of Quantum Chromo-Dynamics, which describes the strong interactions, has two different vacuum states—perturbative vacuum and physical vacuum. Colored quarks and gluons can only exist in physical vacuum and are confined in color neutral hadrons. In 1970s, T.D. Lee et al. predicted that a new state of matter—quark gluon plasma will be formed while the phase transition from physical vacuum to perturbative vacuum happens in high energy nucleus-nucleus collisions. Since then, great progress has been made in the experimental and theoretical fields of heavy ion collisions. In the new century, the relativistic heavy ion collider(RHIC) in the Brookheaven National Laboratory in U.S. with colliding energy above several hundred GeV has started taking data and obtained a lot of new results. Combining all of the experimental results, people believe that partonic(quark and gluon) degree of freedom has been formed in the volume about thousands times that of hadrons. It means that the color confinement of quarks has disappeared and the transition between physical vacuum and perturbative vacuum happened. What's the character of the formed new state of de-confined quark and gluon? How to transfer from normal hadron to de-confined quarks and gluons? These will be the most important research topics in the present and future physics.
The QCD phase diagram predicted by lattice gauge theory is the following: in the region with high baryon density and low temperature the transition between normal hadron matter and QGP is a first order phase transition. As the increase of temperature and decrease of baryon density, the line of the first order phase transition ends at the critical point and in higher temperature and lower density region, there is a cross-over from normal hadron to QGP.
From the current experimental results, people has not found the critical point and the first order phase transition below critical point. In order to study the phase transition, RHIC will run at lower beam energies and GSI in Germany is building new facilities to satisfy the low temperature and high baryon density condition.
Transport models are usually used to study the time and space evolution of heavy ion collisions. The transport model, which is a numerical solution of transport equation, will follow the collision process by inputting the nuclear geometry and reaction cross-section. The multiphase transport model of heavy ion collision includes parton phase and hadron phase and is suitable for the study of phase transition. In this model the partons are allowed to transport until ceasing interactions with other partons at given scattering cross section. By this means the transition between partons and hadrons is a parton-wise behavior instead of a collective one, resulting in individual hadronization time of partons. It's unreasonable that a few partons move freely in a system full of hadrons after most of the partons has already hadronize to hadrons and the perturbative vacuum turned to physical one.
To solve this problem, we need to consider how to realize collective phase transition in transport model. In this thesis, taken the AMPT model as example, we investigate the time evolution of some physical quantities in the model. Assume the system achieves local thermal equilibrium, the temperature of partons and hadrons are extracted respectively by fitting their invariant transverse mass distribution to a thermal + radial flow model. Based on the parton and hadron temperature evolution, we implement a collective sudden phase transition following a supercooling state to the model by requiring all partons hadronize at the same time after the supercooling state. It turns out that the modified model with a sudden phase transition inherits the success of the original one in elliptic flow and is able to reproduce the experimental longitudinal distributions of final state particles better than the original one does. The encouraging results indicate that equilibrium phase transition should be taken into proper account in parton transport models for relativistic heavy ion collisions.
Particle identification is important in experimental physics. In the current heavy ion collisions, higher reconstruction efficiency of strange baryons likeΞandΩis crucial to the precise measurement of elliptic flow and to the confirmation of the discovery of parton degree of freedom. Theorists have predicted that extotic multi-quark state (ΩΩ) of six strange quarks could be formed in quark gluon plasma. In order to find this kind of low yield particles, more efficient particle identification methods are called for.
Artificial neural network is a kind of information processor with nonlinear dynamical properties by simulating the neuron system of human brain. It had been widely used in the fields such as pattern recognition, auto control, image process. In the early 1990s, neural network method was introduced to high energy experimental physics and it is found to be promising in dealing with the problem as track reconstruction, energy cluster reconstruction and particle identification. In this thesis, we will study how to improve the particle identification efficiency by using neural network method. At first, the neural network is applied to quark and gluon jets produced from the Monte Carlo simulation of e~+e~- collision at s~(1/2) = 91.2GeV. From this application, some factors which will affect the performance of neural network are investigated. Then neural network is used to reconstruct the A particles from (sNN)~(1/2) = 200GeV d-Au collision data taken by RHIC STAR detector. Comparing track-cutting method with neural network, we found that the reconstruction efficiency of A particles by neural network method is 29% higher than that of the cutting method, but the signal-background ratio of the reconstruction by neural network method is lower than that of the cutting method. In order to improve the performance of neural network, a kind of re-sampling technique—adaptive boosting algorithm, is combined with neural network. To study the classification ability of boosted neural network, two different cases are considered, one is the two dimensional toy model in which signal and background are separable with irregular boundaries, the other is the Monte Carlo quark and gluon jets samples in which signal and background are overlapped with each other. We found that the boosting technique is able to improve the classification efficiency and signal-background ratio in the first case, i.e. the separable samples, but failed for the second case where there are mixing between signal and background.
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