高能重离子碰撞中重味介子的夸克组合产生
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摘要
量子色动力学(QCD)理论预言,在极高温和高密度的条件下,普通的强子物质会发生相变而形成一种新的物质形态,夸克胶子等离子体(QGP)。宇宙大爆炸理论则认为这种特殊的物质形态存在于宇宙形成的初期阶段。在一般条件下,夸克禁闭于强子中而无法在实验中观测到单个的自由夸克。高能重离子碰撞实验为我们提供了可以产生上述QCD相变的高温高能量密度的实验室环境。近年来,美国Brookhaven国家实验室的相对论重离子对撞机(RHIC)实现了每对核子质心系能量200 GeV的金—金(Au+Au)、铜—铜(Cu+Cu)碰撞实验。实验中观测到的高横动量区域粒子产额的压低和末态强子的集体流效应等实验现象,已经初步证明在RHIC能区发生了退禁闭的QCD相变。目前,欧洲核子研究中心的大型强子对撞机(LHC)将实现每对核子质心系能量5.5 TeV的Pb+Pb对撞,致力于全面研究QGP物质的特性。
在高能重离子碰撞实验中,重味夸克在碰撞初期的硬散射过程中产生,即产生的时间早于发生QGP相变的时间。这些重味夸克在穿越相变产生的热密介质时,与介质发生相互作用或由于胶子辐射而损失能量。由于它们经历整个相变过程,因此携带了大量的丰富的关于热密介质的信息,从而可以作为探测热密介质性质的理想探针。研究RHIC和LHC能区重离子碰撞实验中末态的重味强子是高能物理中的热点问题,是研究退禁闭的QGP物质特性的有效手段之一。本文详细讨论了碰撞末态中的各种重味介子的横动量谱和椭圆流。
研究末态强子的产生机制,有利于帮助人们了解QGP物质的性质和重离子碰撞系统的演化过程。在人们提出的众多强子化机制中,较为成功的有适用于低横动量区域的弦模型和适用于高横动量区域的部分子独立碎裂模型。而在RHIC能区的中等横动量区域,这两种模型在解释一些实验现象时都遇到了困难。近年来,逐步发展和完善起来的夸克重组合模型不仅可以很好地符合RHIC能区的整个横动量区域的粒子横动量谱,还可以解释一些新的实验现象,如Cronin效应,3<ΡΤ< 4 GeV/c区域重子产额反常增加即比值p/π～1,椭圆流的组分夸克数目标度行为等。
本文首次将夸克重组合模型应用于研究RHIC能区和LHC能区重味介子产生的横动量谱以及它们的椭圆流。重组合模型将部分子i碎裂成为强子h的过程分为两步：(1)在重离子碰撞初期的硬散射过程中产生高能量的硬部分子i,在该硬部分子的簇射(shower)中分布有各种“味”的夸克,即簇射部分子；(2)两个或者三个簇射部分子重新组合,形成强子。夸克重组合模型最重要的一步就是将常用的部分子碎裂函数Dih表述成为两个(介子)或者三个(重子)簇射部分子的重组合过程,并唯象地得到簇射部分子的分布。本文将首先通过重建重味介子的碎裂函数,得到这些介子的组分夸克作为簇射部分子的分布。从簇射部分子分布的结果来看,在小动量份额区域(x<0.35),硬部分子c喷注中轻夸克部分子(u、d、s夸克)分布远高于c夸克部分子分布；当x值增加时,该喷注中则会有更多的几率产生c夸克；同时,在硬部分子c喷注中发现c夸克的几率远大于(?)夸克；而在胶子喷注中产生的u、d夸克或者s夸克的几率密度远高于c或b夸克。
碰撞实验末态的观测强子都是由部分子重组合形成的。而部分子有两种来源：热部分子和簇射部分子。因此,部分子的组合形式有：热部分子—热部分子重组合,热部分子—簇射部分子重组合以及簇射部分子—簇射部分子重组合。硬部分子分布中需要考虑它们在穿越热密介质时的能量损失。我们详细讨论了RHIC能区每对核子质心系能量(?)=200 GeV,不同中心度下的Au+Au碰撞实验中的J/ψ横动量谱,其计算结果可以很好地符合PHENIX合作组的实验数据。在较小的横动量区域,介子的产生主要源于热部分子的重组合,在较高横动量区域,占主导地位的是簇射部分子重组合,该部分在理论上等同于部分子碎裂过程的贡献；而在中等横动量区域,介子产生的主要贡献来自于热部分子与簇射部分子的重组合。这也进一步显示了夸克重组合的强子化机制被应用于中等横动量区域的优越性。同时,我们也进一步预言了其他粲介子和B介子的横动量分布,其结果有待实验的检验。
如果考虑同一喷注中的π介子横动量分布,我们可以进一步讨论π-J/ψ的关联。在π作为触发粒子的喷注中,近端的横动量为pa的J/ψ分布在pa>3.8 GeV/c时随触发粒子横动量pt的增加而增加；在较小的pa区域,其结果相反；并且其变化趋势不随中心度的变化而变化。另一方面,远端的J/ψ产额在整个横动量区域都是单调递减的,并且其分布在边缘碰撞时将变得平滑。引起这种变化的主要原因在于π与J/ψ砂截然不同的碎裂函数。
考虑硬部分子分布与方位角的依赖关系,可以得到反映末态粒子各向异性的一个重要参数：椭圆流参数v2。J/ψ的v2值在误差范围内可以符合PHENIX合作组的实验数据。我们发现D介子的v2值大于J/ψ的v2值,这种现象不符合椭圆流参数的组分夸克数目标度行为,因为在重组合模型中,D介子的横动量基本来自于c夸克的横动量贡献,因为c夸克的质量远大于另一个组分夸克(轻夸克)的质量。
当系统的能量增加,例如LHC能区,我们必须考虑来自于两个不同喷注的簇射部分子的重组合贡献。此项贡献依赖于两相邻喷注的重叠几率。当重叠几率足够小或足够大时,J/ψ的v2值都保持为一常数;而当不同来源的簇射部分子重组合贡献与来自于同一喷注的簇射部分子重组合贡献可比时,所对应的v2值随pT的增加而减小,其趋势与微扰QCD理论预言的结果相似。
Quantum Chromo-dynamics (QCD) theory predicts a phase transition from hadronic matter to deconfined, locally thermalized Quark-Gluon Plasma (QGP) at very high temperature or high energy. QGP is believed to exist at the early stage of the formation of the universe before free quarks and gluons combined into hadrons. In general conditions, quarks are confined in the hadrons so that people can not detect a free quark in the laboratory. Heavy ion collisions provide a high temperature or a high energy density environment to create and search for the QGP matter. In recent years the Relativistic Heavy Ion Collider (RHIC) located at Brookhaven National Laboratory has achieved great processes through Au+Au and Cu+Cu collisions at center-of-mass energy (?)= 200 GeV. Lots of experimental phenomena detected in the lab such as the suppression of the particle yield in the region of high transverse momentum, the collective flow effect, etc. have preliminarily proved the production of the deconfined QGP phase transition. Now Pb+Pb collisions with higher energy of (?)= 5.5 TeV at the Large Hadron Collider (LHC) are also dedicated to study the character of QGP and the evolution process of the colliding system. Since heavy quarks are produced in the initial hard scattering processes before the formation of QGP phase transition, they are sensitive to probe the medium formed in the collisions as they may lose energy by gluon radiation during propagating through the medium and then carry abundant information of QGP. Heavy flavored hadron production at the final state at RHIC and LHC is a subject of current interest for understanding the.quark-gluon interaction. In this thesis we study the production of all kinds of heavy flavored hadrons and the elliptic flow parameter of these hadrons.
Study of the particle production scheme is an important tool to understand the character of QGP and the evolution of the parton system created by the heavy ion collisions. There are two classical models to describe the hadronization scheme:the string model which is appropriate for hadrons with low pT and the parton individual fragmentation model which is successful to describe the hadron production at high pT.While these tow models are failed to be applied to explain many experimental facts at intermediate pT at RHIC energy. Recently the developed recombination model has achieved great progress in describing the particle production at any pT at RHIC and explaining the new experimental phenomena such as the Cronin effect, the ratio of p/π～1 at 3< pT< 4 GeV/c, the scaling law of elliptic flow in the number of constituents, etc..
It's the first time for us to apply the recombination model to study the heavy flavored meson productions and their elliptic flow at RHIC and LHC. The process of a parton i fragmentation into a hadron h can be divided into two steps:(1) a hard parton i is produced by the hard scattering at the initial stage of the heavy ion collisions. And there are shower partons with all kinds of flavors distributed in the parton shower. (2) Two or three partons recombine together to form a hadron. The most important step in the model is to get the shower parton distributions (SPD) through describing the well-known fragmentation functions as the recombination of the shower partons. In this thesis we calculate the SPDs related with the heavy flavored meson productions by reproducing their fragmentation functions. We find that the distribution of light quarks initiated from hard parton c is higher than that of c quark in the region of small momentum fraction x< 0.35, and lower when x is large. In other words, there are more light quarks than charm quarks at low momentum fraction. The distribution of c quark created in a c jet is much higher than that of c quark in almost the whole region. A gluon jet has a density of produced light or strange quarks higher than that of charm or beauty quarks.
The detected hadron at the final stage are all formed by the recombination of partons. Since there are two sources of the partons:thermal partons and shower partons, the hadron produc-tion can be expressed as the sum of contributions of thermal-thermal, thermal-shower and shower-shower recombinations. The energy loss effect of the parton propagating through the dense medium is considered in the hard parton distributions. We discuss the transverse momentum spectra of J/φin Au+Au collisions with different centralities at (?)= 200 GeV at RHIC, and the cal-culated results can fit the experimental data from PHENIX collaboration well. We find that at low transverse momentum range the main contribution comes from thermal-thermal recombina-tion and at high pT shower-shower recombination equivalent with the process of fragmentation is dominant. While the recombination of thermal-shower partons plays a major role in the region of intermediate momentum, which demonstrates the advantage of the recombination model. Also, we predict the momentum spectra of other charmed mesons and B mesons which will be tested by further experiments.
Considering the production ofπand J/φin the same jet, we discuss the di-hadron correlation ofπ-J/φ. The correlation of the particle J/φwith pa associated with the trigger particleπwith pt on the near side shows the near-side yield increases with pt for pa> 3.8 GeV/c, while this trend is reversed in the region of low pa, and the shape of the distribution is independent of the centrality. On the other hand, the away-side yield becomes higher as pt increases, and the trend becomes smoother and similar to that of the near-side in more peripheral collisions. The difference is mainly caused by the significantly different fragmentation functions for J/φandπ.
We get another important parameter, the elliptic flow parameterυ2 which reflects the az-imuthal anisotropy of the particle if we get the azimuthal angle dependence of the hard parton distribution. The value ofυ2 for J/φcan fit the experimental data from PHENIX collaboration. Andυ2 for D meson is higher than that for J/φ, which is not consistent with the number of quark (NQ) scaling ofυ2.Because in the model the momentum of D0 or Ds comes mainly form charm quark due to the unequal constituent quark masses, we get differentυ2 for J/φand D0 or Ds
At higher energy such as LHC, the contribution from the recombination of shower partons from two different jets must be taken into account. And this term depends on the overlap probability between the two neighboring jets. The values ofυ2 for J/φmaintain as constants if the overlap probability is small enough or becomes quite large. When the contributions to the flow from the recombination of shower partons from two different jets and the recombination of shower partons from the same jets are comparative, the results ofυ2 decease with increasing pT which is very similar to the theory predictions based on the jet energy loss in perturbative QCD.
在高能重离子碰撞实验中,重味夸克在碰撞初期的硬散射过程中产生,即产生的时间早于发生QGP相变的时间。这些重味夸克在穿越相变产生的热密介质时,与介质发生相互作用或由于胶子辐射而损失能量。由于它们经历整个相变过程,因此携带了大量的丰富的关于热密介质的信息,从而可以作为探测热密介质性质的理想探针。研究RHIC和LHC能区重离子碰撞实验中末态的重味强子是高能物理中的热点问题,是研究退禁闭的QGP物质特性的有效手段之一。本文详细讨论了碰撞末态中的各种重味介子的横动量谱和椭圆流。
研究末态强子的产生机制,有利于帮助人们了解QGP物质的性质和重离子碰撞系统的演化过程。在人们提出的众多强子化机制中,较为成功的有适用于低横动量区域的弦模型和适用于高横动量区域的部分子独立碎裂模型。而在RHIC能区的中等横动量区域,这两种模型在解释一些实验现象时都遇到了困难。近年来,逐步发展和完善起来的夸克重组合模型不仅可以很好地符合RHIC能区的整个横动量区域的粒子横动量谱,还可以解释一些新的实验现象,如Cronin效应,3<ΡΤ< 4 GeV/c区域重子产额反常增加即比值p/π～1,椭圆流的组分夸克数目标度行为等。
本文首次将夸克重组合模型应用于研究RHIC能区和LHC能区重味介子产生的横动量谱以及它们的椭圆流。重组合模型将部分子i碎裂成为强子h的过程分为两步：(1)在重离子碰撞初期的硬散射过程中产生高能量的硬部分子i,在该硬部分子的簇射(shower)中分布有各种“味”的夸克,即簇射部分子；(2)两个或者三个簇射部分子重新组合,形成强子。夸克重组合模型最重要的一步就是将常用的部分子碎裂函数Dih表述成为两个(介子)或者三个(重子)簇射部分子的重组合过程,并唯象地得到簇射部分子的分布。本文将首先通过重建重味介子的碎裂函数,得到这些介子的组分夸克作为簇射部分子的分布。从簇射部分子分布的结果来看,在小动量份额区域(x<0.35),硬部分子c喷注中轻夸克部分子(u、d、s夸克)分布远高于c夸克部分子分布；当x值增加时,该喷注中则会有更多的几率产生c夸克；同时,在硬部分子c喷注中发现c夸克的几率远大于(?)夸克；而在胶子喷注中产生的u、d夸克或者s夸克的几率密度远高于c或b夸克。
碰撞实验末态的观测强子都是由部分子重组合形成的。而部分子有两种来源：热部分子和簇射部分子。因此,部分子的组合形式有：热部分子—热部分子重组合,热部分子—簇射部分子重组合以及簇射部分子—簇射部分子重组合。硬部分子分布中需要考虑它们在穿越热密介质时的能量损失。我们详细讨论了RHIC能区每对核子质心系能量(?)=200 GeV,不同中心度下的Au+Au碰撞实验中的J/ψ横动量谱,其计算结果可以很好地符合PHENIX合作组的实验数据。在较小的横动量区域,介子的产生主要源于热部分子的重组合,在较高横动量区域,占主导地位的是簇射部分子重组合,该部分在理论上等同于部分子碎裂过程的贡献；而在中等横动量区域,介子产生的主要贡献来自于热部分子与簇射部分子的重组合。这也进一步显示了夸克重组合的强子化机制被应用于中等横动量区域的优越性。同时,我们也进一步预言了其他粲介子和B介子的横动量分布,其结果有待实验的检验。
如果考虑同一喷注中的π介子横动量分布,我们可以进一步讨论π-J/ψ的关联。在π作为触发粒子的喷注中,近端的横动量为pa的J/ψ分布在pa>3.8 GeV/c时随触发粒子横动量pt的增加而增加；在较小的pa区域,其结果相反；并且其变化趋势不随中心度的变化而变化。另一方面,远端的J/ψ产额在整个横动量区域都是单调递减的,并且其分布在边缘碰撞时将变得平滑。引起这种变化的主要原因在于π与J/ψ砂截然不同的碎裂函数。
考虑硬部分子分布与方位角的依赖关系,可以得到反映末态粒子各向异性的一个重要参数：椭圆流参数v2。J/ψ的v2值在误差范围内可以符合PHENIX合作组的实验数据。我们发现D介子的v2值大于J/ψ的v2值,这种现象不符合椭圆流参数的组分夸克数目标度行为,因为在重组合模型中,D介子的横动量基本来自于c夸克的横动量贡献,因为c夸克的质量远大于另一个组分夸克(轻夸克)的质量。
当系统的能量增加,例如LHC能区,我们必须考虑来自于两个不同喷注的簇射部分子的重组合贡献。此项贡献依赖于两相邻喷注的重叠几率。当重叠几率足够小或足够大时,J/ψ的v2值都保持为一常数;而当不同来源的簇射部分子重组合贡献与来自于同一喷注的簇射部分子重组合贡献可比时,所对应的v2值随pT的增加而减小,其趋势与微扰QCD理论预言的结果相似。
Quantum Chromo-dynamics (QCD) theory predicts a phase transition from hadronic matter to deconfined, locally thermalized Quark-Gluon Plasma (QGP) at very high temperature or high energy. QGP is believed to exist at the early stage of the formation of the universe before free quarks and gluons combined into hadrons. In general conditions, quarks are confined in the hadrons so that people can not detect a free quark in the laboratory. Heavy ion collisions provide a high temperature or a high energy density environment to create and search for the QGP matter. In recent years the Relativistic Heavy Ion Collider (RHIC) located at Brookhaven National Laboratory has achieved great processes through Au+Au and Cu+Cu collisions at center-of-mass energy (?)= 200 GeV. Lots of experimental phenomena detected in the lab such as the suppression of the particle yield in the region of high transverse momentum, the collective flow effect, etc. have preliminarily proved the production of the deconfined QGP phase transition. Now Pb+Pb collisions with higher energy of (?)= 5.5 TeV at the Large Hadron Collider (LHC) are also dedicated to study the character of QGP and the evolution process of the colliding system. Since heavy quarks are produced in the initial hard scattering processes before the formation of QGP phase transition, they are sensitive to probe the medium formed in the collisions as they may lose energy by gluon radiation during propagating through the medium and then carry abundant information of QGP. Heavy flavored hadron production at the final state at RHIC and LHC is a subject of current interest for understanding the.quark-gluon interaction. In this thesis we study the production of all kinds of heavy flavored hadrons and the elliptic flow parameter of these hadrons.
Study of the particle production scheme is an important tool to understand the character of QGP and the evolution of the parton system created by the heavy ion collisions. There are two classical models to describe the hadronization scheme:the string model which is appropriate for hadrons with low pT and the parton individual fragmentation model which is successful to describe the hadron production at high pT.While these tow models are failed to be applied to explain many experimental facts at intermediate pT at RHIC energy. Recently the developed recombination model has achieved great progress in describing the particle production at any pT at RHIC and explaining the new experimental phenomena such as the Cronin effect, the ratio of p/π～1 at 3< pT< 4 GeV/c, the scaling law of elliptic flow in the number of constituents, etc..
It's the first time for us to apply the recombination model to study the heavy flavored meson productions and their elliptic flow at RHIC and LHC. The process of a parton i fragmentation into a hadron h can be divided into two steps:(1) a hard parton i is produced by the hard scattering at the initial stage of the heavy ion collisions. And there are shower partons with all kinds of flavors distributed in the parton shower. (2) Two or three partons recombine together to form a hadron. The most important step in the model is to get the shower parton distributions (SPD) through describing the well-known fragmentation functions as the recombination of the shower partons. In this thesis we calculate the SPDs related with the heavy flavored meson productions by reproducing their fragmentation functions. We find that the distribution of light quarks initiated from hard parton c is higher than that of c quark in the region of small momentum fraction x< 0.35, and lower when x is large. In other words, there are more light quarks than charm quarks at low momentum fraction. The distribution of c quark created in a c jet is much higher than that of c quark in almost the whole region. A gluon jet has a density of produced light or strange quarks higher than that of charm or beauty quarks.
The detected hadron at the final stage are all formed by the recombination of partons. Since there are two sources of the partons:thermal partons and shower partons, the hadron produc-tion can be expressed as the sum of contributions of thermal-thermal, thermal-shower and shower-shower recombinations. The energy loss effect of the parton propagating through the dense medium is considered in the hard parton distributions. We discuss the transverse momentum spectra of J/φin Au+Au collisions with different centralities at (?)= 200 GeV at RHIC, and the cal-culated results can fit the experimental data from PHENIX collaboration well. We find that at low transverse momentum range the main contribution comes from thermal-thermal recombina-tion and at high pT shower-shower recombination equivalent with the process of fragmentation is dominant. While the recombination of thermal-shower partons plays a major role in the region of intermediate momentum, which demonstrates the advantage of the recombination model. Also, we predict the momentum spectra of other charmed mesons and B mesons which will be tested by further experiments.
Considering the production ofπand J/φin the same jet, we discuss the di-hadron correlation ofπ-J/φ. The correlation of the particle J/φwith pa associated with the trigger particleπwith pt on the near side shows the near-side yield increases with pt for pa> 3.8 GeV/c, while this trend is reversed in the region of low pa, and the shape of the distribution is independent of the centrality. On the other hand, the away-side yield becomes higher as pt increases, and the trend becomes smoother and similar to that of the near-side in more peripheral collisions. The difference is mainly caused by the significantly different fragmentation functions for J/φandπ.
We get another important parameter, the elliptic flow parameterυ2 which reflects the az-imuthal anisotropy of the particle if we get the azimuthal angle dependence of the hard parton distribution. The value ofυ2 for J/φcan fit the experimental data from PHENIX collaboration. Andυ2 for D meson is higher than that for J/φ, which is not consistent with the number of quark (NQ) scaling ofυ2.Because in the model the momentum of D0 or Ds comes mainly form charm quark due to the unequal constituent quark masses, we get differentυ2 for J/φand D0 or Ds
At higher energy such as LHC, the contribution from the recombination of shower partons from two different jets must be taken into account. And this term depends on the overlap probability between the two neighboring jets. The values ofυ2 for J/φmaintain as constants if the overlap probability is small enough or becomes quite large. When the contributions to the flow from the recombination of shower partons from two different jets and the recombination of shower partons from the same jets are comparative, the results ofυ2 decease with increasing pT which is very similar to the theory predictions based on the jet energy loss in perturbative QCD.
引文
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