QCD物质相结构及临界行为若干问题的模型理论研究
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摘要
量子色动力学(QCD)是描述夸克层次上的强相互作用动力学基本理论。在有限温度有限密度下,QCD物质具有非常丰富的相结构,如强子物质相,夸克胶子等离子体相及超导超流相等。研究不同相之间的相变及临界现象,确定相边界及临界点位置等,是当前高能物理研究领域里的重要课题。一般来讲,直接从QCD拉式量出发进行研究,在高温高密条件下,可以采用微扰论的方法。在非微扰区域,通过格点计算或建立具有QCD对称性的有效模型来讨论QCD物质的热力学性质及相关计算方法等。本论文基于QCD有效模型,讨论了有限重子数密度下QCD临界点位置的确定、不同临界行为的过渡区域；有限同位旋密度下三种相变的相互影响及在π超流相的BEC-BCS过渡。
本文的前三章简要评述了相关的工作基础。首先,我们对已有的QCD物质相结构的研究作了简单回顾。然后,介绍了具有QCD对称性的两种有效模型,Nambu-Jona-Lasinio (NJL)模型和Polyakov-NJL (PNJL)模型。NJL模型是四费米子直接相互作用,具有QCD的手征对称性。PNJL模型在NJL模型基础上,引入静态胶子场背景,将夸克的手征凝聚与Polyakov圈耦合起来,兼具QCD手征性和禁闭性质。具体计算是在有限温度场论框架下进行的。
本文的后半部,讨论了具体的研究成果。我们用朗道相变理论,系统分析了两味NJL模型在有限温度有限重子数密度下的相结构,给出三维空间T-μ-m0中的相图。清楚地显示出三临界点、临界结点以及普通临界点的区别和联系,为接下来分析临界现象作准备。考虑到手征极限下三临界点的特殊性,我们分析了沿不同相变线趋近它时热力学量的临界行为。结果表明,在三临界点邻域内,存在从φ4-φ6临界行为的过渡区域,且给出了不同临界行为的区域。进一步研究表明,沿一级相变线去趋近三临界点时,临界指数需要进行Fisher重整化。
通过能量扫描寻找QCD临界点位置,一直是高能重离子碰撞实验的目标之一由于临界点是一级相变的终止点,我们考虑沿一级相变线进行能量扫描去接近QCD临界点的方法。本文的分析证实,不仅在手征对称破缺相有热π介子存在,而且在手征对称恢复相,除了有夸克反夸克外,必然会存在热π介子被激发的区域。考虑到一级相变线上系统处于两相共存状态,文中分析了这种特征。序参量及相关物理量如π介子质量等具有两个物理值,但到临界点处两个物理值重合。热π介子在两相的质量差别,会使得在两相介子的丰度不同,从而π介子衰变的产额也不同。但到临界点这些差别消失。我们期待这种图像能为实验上探索相边界和临界点提供有益的启示。
最后,我们在PNJL模型框架下研究了同位旋化学势效应。讨论了手征相变、退禁闭相变和π超流相变的相互影响,计算了超流相的介子激发谱,并获得相应的T-μI,相结构。结果表明,禁闭性扩大了手征凝聚和π凝聚的范围,并且影响了热力学系统的集体激发模式；T-μI相图被分为四种物态区域,即强子相、夸克胶子等离子体相、BEc超流相和BCS超流相。在π超流相,当同位旋化学势大小等于两倍夸克有效质量时,存在BEC-BCS的过渡行为,这是密度引起的效应。
Quantum Chromodynamics (QCD) is a basic dynamical theory describing the strong interaction on the quark level. QCD matter has rich phase structures at finite temper-ature and density. For instance, the hadronic matter phase, the quark-gluon plasma, superconductor and superfluidity etc. Studying the transitions of different phases and the critical phenomena, determining the phase boundary and the position of QCD criti-cal point, are important issues of high energy heavy-ion collision. Generally speaking, if calculate from the QCD Lagrangian directly, we could adopt method of the perturbative theory at very high temperature and density. In the nonperturbative region, one discuss the thermodynamical properties of QCD matter and related calculated methods through lattice calculation or establishing effective models which have corresponding symmetric properties of QCD. This paper is based on the QCD effective models, and discuss the fol-lowing contents:the determination of the position of QCD critical point at finite baryon density; the crossover region of different critical behavior; the inter-influence of three phase transitions at finite isospin density and the BEC-BCS crossover in the superfluidity phase.
The first three chapters subject to the basis corresponding to our work. Firstly, we have a brief review of the past studies of QCD phase structures. Then, we introduce two effective models which have the similar symmetry of QCD Lagrangian—the Nambu-Jona-Lasinio (NJL) model and the Polyakov-NJL (PNJL) model. The former is of four fermions point-like interaction and has the chiral symmetry of QCD Lagrangian. The latter is based on the NJL model and introduce a static gluon background. The PNJL model couples the chiral condensate and the Polyakov loop which both contain the quark contribution. And it has the chiral and confinement properties of QCD theory. The calculations are in the frame of the finite temperature field theory.
The back part of our paper subject to the results of our study. Using the Landau the-ory of phase transitions, we analyse the phase structure of two flavor NJL model at finite temperature and finite baryon number chemical potential and give the phase diagram in the 3-dimension space of T-μ-m0. The phase diagram clearly show the difference and connection of tricritical point, critical end point and common critical point. And it also behaves as a preparation of the analysis of critical phenomena in the following. Consider-ing the special characteristics of the tricritical point at chiral limit, we analyse the critical behavior of thermodynamical quantities at the tricritical point along different phase tran-sition lines. The result shows that in the vicinity of the tricritical point, there are crossover regions ofφ4-φ6 critical behavior. We display the regions of different critical behavior. A further study shows that, the critical exponents need the Fisher renormalization when one approach the tricritical point along the first-order phase transition line.
By means of energy scan to locate the QCD critical point is always one of objectives of high energy heavy ion collision experiment. Since the critical point is the end of the first order phase transition line, we consider the method of approaching the QCD critical point along the first order phase transition line in the energy scan. Our study shows that, the thermalπmesons exist not only in the chiral symmetry broken phase, but also in the chiral symmetry restored phase where the main degrees of freedom are quark and antiquarks. On the first order phase transition line the thermodynamical system is in the two phases coexistence. The character leads the order parameter and corresponding physical quantities such as the mass ofπetc. have two physical values. At the critical point these two values equal. The mass difference of the thermalπmeson in two phases result in the difference of pion abundance. And further the decay production ofπdiffers. At the critical point the difference disappears. We expect this physical picture would provide helpful enlightenment for exploring the phase boundary and critical point in experiment.
At last, we study the effect of isospin chemical potential in the frame of the PNJL model. We discuss the inter-influence of the chiral, deconfinement andπsuperfluidity phase transitions, calculate the meson excitation spectra in the superfluidity phase and obtain the corresponding T-μI phase structure. The results show that the confinement property enlarges the regions of chiral condensate andπcondensate and influences the collective excitation modes of the thermodynamical system. The T-μI phase diagram is divided into four matter-state parts:the hadronic phase, the quark gluon plasma phase, the BEC superfluidity phase and the BCS superfluidity phase. In the pion superfluidity phase, when the value of the isospin chemical potential equals the double quark effective mass, there exists BEC-BCS crossover. This is the density effect.
本文的前三章简要评述了相关的工作基础。首先,我们对已有的QCD物质相结构的研究作了简单回顾。然后,介绍了具有QCD对称性的两种有效模型,Nambu-Jona-Lasinio (NJL)模型和Polyakov-NJL (PNJL)模型。NJL模型是四费米子直接相互作用,具有QCD的手征对称性。PNJL模型在NJL模型基础上,引入静态胶子场背景,将夸克的手征凝聚与Polyakov圈耦合起来,兼具QCD手征性和禁闭性质。具体计算是在有限温度场论框架下进行的。
本文的后半部,讨论了具体的研究成果。我们用朗道相变理论,系统分析了两味NJL模型在有限温度有限重子数密度下的相结构,给出三维空间T-μ-m0中的相图。清楚地显示出三临界点、临界结点以及普通临界点的区别和联系,为接下来分析临界现象作准备。考虑到手征极限下三临界点的特殊性,我们分析了沿不同相变线趋近它时热力学量的临界行为。结果表明,在三临界点邻域内,存在从φ4-φ6临界行为的过渡区域,且给出了不同临界行为的区域。进一步研究表明,沿一级相变线去趋近三临界点时,临界指数需要进行Fisher重整化。
通过能量扫描寻找QCD临界点位置,一直是高能重离子碰撞实验的目标之一由于临界点是一级相变的终止点,我们考虑沿一级相变线进行能量扫描去接近QCD临界点的方法。本文的分析证实,不仅在手征对称破缺相有热π介子存在,而且在手征对称恢复相,除了有夸克反夸克外,必然会存在热π介子被激发的区域。考虑到一级相变线上系统处于两相共存状态,文中分析了这种特征。序参量及相关物理量如π介子质量等具有两个物理值,但到临界点处两个物理值重合。热π介子在两相的质量差别,会使得在两相介子的丰度不同,从而π介子衰变的产额也不同。但到临界点这些差别消失。我们期待这种图像能为实验上探索相边界和临界点提供有益的启示。
最后,我们在PNJL模型框架下研究了同位旋化学势效应。讨论了手征相变、退禁闭相变和π超流相变的相互影响,计算了超流相的介子激发谱,并获得相应的T-μI,相结构。结果表明,禁闭性扩大了手征凝聚和π凝聚的范围,并且影响了热力学系统的集体激发模式；T-μI相图被分为四种物态区域,即强子相、夸克胶子等离子体相、BEc超流相和BCS超流相。在π超流相,当同位旋化学势大小等于两倍夸克有效质量时,存在BEC-BCS的过渡行为,这是密度引起的效应。
Quantum Chromodynamics (QCD) is a basic dynamical theory describing the strong interaction on the quark level. QCD matter has rich phase structures at finite temper-ature and density. For instance, the hadronic matter phase, the quark-gluon plasma, superconductor and superfluidity etc. Studying the transitions of different phases and the critical phenomena, determining the phase boundary and the position of QCD criti-cal point, are important issues of high energy heavy-ion collision. Generally speaking, if calculate from the QCD Lagrangian directly, we could adopt method of the perturbative theory at very high temperature and density. In the nonperturbative region, one discuss the thermodynamical properties of QCD matter and related calculated methods through lattice calculation or establishing effective models which have corresponding symmetric properties of QCD. This paper is based on the QCD effective models, and discuss the fol-lowing contents:the determination of the position of QCD critical point at finite baryon density; the crossover region of different critical behavior; the inter-influence of three phase transitions at finite isospin density and the BEC-BCS crossover in the superfluidity phase.
The first three chapters subject to the basis corresponding to our work. Firstly, we have a brief review of the past studies of QCD phase structures. Then, we introduce two effective models which have the similar symmetry of QCD Lagrangian—the Nambu-Jona-Lasinio (NJL) model and the Polyakov-NJL (PNJL) model. The former is of four fermions point-like interaction and has the chiral symmetry of QCD Lagrangian. The latter is based on the NJL model and introduce a static gluon background. The PNJL model couples the chiral condensate and the Polyakov loop which both contain the quark contribution. And it has the chiral and confinement properties of QCD theory. The calculations are in the frame of the finite temperature field theory.
The back part of our paper subject to the results of our study. Using the Landau the-ory of phase transitions, we analyse the phase structure of two flavor NJL model at finite temperature and finite baryon number chemical potential and give the phase diagram in the 3-dimension space of T-μ-m0. The phase diagram clearly show the difference and connection of tricritical point, critical end point and common critical point. And it also behaves as a preparation of the analysis of critical phenomena in the following. Consider-ing the special characteristics of the tricritical point at chiral limit, we analyse the critical behavior of thermodynamical quantities at the tricritical point along different phase tran-sition lines. The result shows that in the vicinity of the tricritical point, there are crossover regions ofφ4-φ6 critical behavior. We display the regions of different critical behavior. A further study shows that, the critical exponents need the Fisher renormalization when one approach the tricritical point along the first-order phase transition line.
By means of energy scan to locate the QCD critical point is always one of objectives of high energy heavy ion collision experiment. Since the critical point is the end of the first order phase transition line, we consider the method of approaching the QCD critical point along the first order phase transition line in the energy scan. Our study shows that, the thermalπmesons exist not only in the chiral symmetry broken phase, but also in the chiral symmetry restored phase where the main degrees of freedom are quark and antiquarks. On the first order phase transition line the thermodynamical system is in the two phases coexistence. The character leads the order parameter and corresponding physical quantities such as the mass ofπetc. have two physical values. At the critical point these two values equal. The mass difference of the thermalπmeson in two phases result in the difference of pion abundance. And further the decay production ofπdiffers. At the critical point the difference disappears. We expect this physical picture would provide helpful enlightenment for exploring the phase boundary and critical point in experiment.
At last, we study the effect of isospin chemical potential in the frame of the PNJL model. We discuss the inter-influence of the chiral, deconfinement andπsuperfluidity phase transitions, calculate the meson excitation spectra in the superfluidity phase and obtain the corresponding T-μI phase structure. The results show that the confinement property enlarges the regions of chiral condensate andπcondensate and influences the collective excitation modes of the thermodynamical system. The T-μI phase diagram is divided into four matter-state parts:the hadronic phase, the quark gluon plasma phase, the BEC superfluidity phase and the BCS superfluidity phase. In the pion superfluidity phase, when the value of the isospin chemical potential equals the double quark effective mass, there exists BEC-BCS crossover. This is the density effect.
引文
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