相对论重离子碰撞中直接光子产生和QCD真空中夸克虚度的研究
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摘要
二十世纪七十年代,李政道和G.C.Wick预言通过相对论高能重离子碰撞有可能在一定的空间区域内形成高温高密系统,使能量密度达到产生夸克解禁闭的阈值,从而形成一种新的物质形态—夸克胶子等离子体(Quark Gluon Plasma—QGP)。这一预言极大地推动了重离子碰撞理论和实验的发展,使其成为物理学的一个主流研究方向。上世纪八十年代美国布鲁克海文国家实验室(BNL)的AGS和欧洲核子中心(CERN)的SPS开始运行,2000年相对论重离子对撞机(RHIC)在BNL的建成运行,至今已经积累了大量实验数据。通过对这些实验数据的分析和计算表明：在RHIC的Au+Au对心碰撞实验中已经产生了一种非常粘稠的不能用强子自由度来描述的部分子物质,而这种部分子极有可能是一种强耦合的夸克胶子等离子体(strongly coupled Quark Gluon Plasma—sQGP)。预计已经在CERN运行的大型强子对撞机(LHC)将产生寿命更长的QGP物质,这为寻找QGP及研究这种新的物质形态提供了前所未有的机会。
通过多年的研究,人们相继提出了一些物理观测量,期望通过这些物理观测量来判定夸克胶子等离子体是否形成,例如：奇异粒子对产额的增长,J/ψ压低,集体流效应等等。其中,大横动量的光子产生被认为是研究QGP物质形态的理想指针信号。光子作为指针信号的优点在于：光子与其它粒子间的相互作用为电磁相互作用,电磁耦合常数(αe=1/(137))非常小,所以平均自由程比较大,产生的光子不与其它粒子发生强相互作用,能够离开碰撞区域被探测到,并携带QGP的热力学信息。
在核子-核子碰撞中产生的光子根据反应过程可分为：由软过程产生的软光子,即衰变光子；由硬过程产生的硬光子,包括直接光子(组分部分子直接通过湮灭过程或康普顿过程产生的光子)和碎裂光子。在核-核碰撞中,由于核介质效应,产生的光子根据反应过程可分为：由软过程产生的软光子,包括热光子和衰变光子：由硬过程产生的硬光子,包括直接光子和碎裂光子,以及2003年由R.J.Fries提出的一个硬过程产生的部分子与高温高密介质中的热部分子通过康普顿过程或正反夸克湮灭过程产生的光子,即喷注-光子转化(Jet-Photon conversion)。我们主要感兴趣的是由硬过程产生的光子。在p+p碰撞中,大横动量的光子谱主要由直接光子和碎裂光子组成。而在A+A碰撞中,强作用介质使得大横动量光子谱主要由直接光子、碎裂光子和喷注-光子转化产生。其中碎裂光子和喷注-光子转化都是由部分子喷注产生的,而部分子喷注在穿过高温高密介质时会发生多重散射诱发胶子辐射损失能量,因此和同一能量下的p+p碰撞产生的光子谱相比,A+A碰撞产生的光子谱将更复杂。这其中不但有初态的核效应,还有末态部分子喷注能量损失效应,以及由于强作用介质导致的其他光子产生,例如：喷注-光子转化。
在本文中,我们首先研究了RHIC高能核-核碰撞的直接光子产生。原来的高能核-核碰撞产生直接光子研究中,人们只计算到了光子产生的领头阶(LO),对于高阶修正的贡献是通过一个因子K人为引入的。我们通过直接计算核-核碰撞次领头阶(NLO)的贡献,考察了RHIC的Au+Au碰撞直接光子产生,避免了引入K因子计算高阶修正贡献的不确定性。在次领头阶(NLO)部分子模型的基础上,我们分别在(1+1)维Bjorken模型和(3+1)维理想流体力学模型下定量地研究了在RHIC能区对心度为0-10%的Au+Au碰撞的光子谱,并给出核修正因子RAA。通过对光子谱的研究,我们得到如下结果：热光子贡献主要在小pT区域,随着PT的增加热光子贡献迅速减小；在大PT区域,以直接光子的贡献为主,部分子的能量损失使得由碎裂光子和喷注-光子转化的贡献被大大压低。此外,我们还研究了核修正因子RAA。在横动量4GeV大横动量(PT>14 GeV)区问理论结果与实验有明显偏离。在大横动量区问理论结果与实验不一致也许与实验上p+p测量在大横动量区间有比较大的实验误差有关。因此,我们期待大横动量区域更进一步的实验结果能够检验我们的理论。
木文的第二部分研究工作是在次领头阶(NLO)部分子模型的基础上,通过采用不同的初态核效应参数化形式,定量研究了在RHIC和LHC能区p十A和对心A+A碰撞中直接光子和中性π介子的核修正因子RpA和RAA。在考虑由于初态核介质效应引起部分子分布函数的修正时,我们采用了EKS,EPS,DS和HKN四种参数化形式。我们的研究结果表明：无论在RHIC还是LHC能区,对心A+A碰撞中直接光子的核修正因子RaγA是辨别现有的各种初态核效应参数的最有效工具。
本文的第三部分研究工作是基于“彩虹”近似,求解Dyson—Schwinger方程,研究QCD真空中夸克的虚度。QCD非定域的真空凝聚描述了在非微扰QCD真空中夸克和胶子的分布。物理上讲,这意味着真空中的夸克和胶子有非零的平均平方动量,此平均平方动量称之为夸克的虚度。夸克的虚度是由定域的夸克胶子的混合凝聚值与定域的夸克凝聚值之比决定的。我们基于有效的胶子传播子,在三组不同参数下(χ和△),求解夸克传播子的Dyson—Schwinger方程,计算了定域夸克真空凝聚值和定域夸克胶子混合真空凝聚值。利用计算的凝聚值,得到了QCD真空中夸克的虚度λq。我们的理论预言值与QCD求和规则、格点规范和瞬子模型等的理论计算结果一致。在具体计算中,我们发现对于有效的胶子传播子,(?)其第一项对夸克虚度的贡献是主要的,第二项的贡献可以忽略。
In 1970s, T.D. Lee and G.C.Wick predicted that a new state of matter—Quark Gluon Plasma(QGP) could be formed in relativistic heavy ion collisions. Since then, great progress has been made in the experimental and theoretical fields of heavy ion collisions. In 1980s, several experiments performed at AGS in the Brookheaven National Laboratory (BNL) in U.S. and at SPS in CERN in Europe. In the new century, the relativistic heavy ion collider (RHIC) in BNL with energy about 200 GeV has started taking data and obtained a lot of new results. Combining all of the experimental results, people believe that a strongly coupled QGP has been formed in heavy ion collisions. A giant accelerator known as Large Hadron Collider (LHC) at CERN has been in operation and will provide many new insights about the properties of QGP and the theory of strong interactions.
The QGP is a state of matter consisting of deconfined quarks and gluons. It is hypothesized to exist at high baryon densities and high temperature. These circumstances are available for experiments in heavy ion collisions, and even there the presence of the QGP cannot be measured directly. So far many signals have been proposed to probe the formation and the properties of QGP, such as:heavy quark enhancement, J/ψsuppression, collective flow, and so on. Among them, high pΤphoton production is a good signal to study the properties of QGP. Unlike hadrons, photons are gauge bosons in electromagnetic interaction in nature, (αe=(?)), they interact weakly with hadrons and their mean free path is large. As a result, once produced, the photons do not suffer further interaction with the medium and carry the information about the circumstances of their production to the detector.
In nucleon-nucleon collisions, photons can be categorized into the soft photons which come from soft processes, such as:decay photons, and the hard photons which come from hard pro-cesses, such as:direct photons and fragmentation photons. In nucleus-nucleus collisions, due to the effect of the medium, photons can be categorized into thermal photons which emitted from a thermalized plasma, decay photons which decay from the hadrons such as pions and etas, and hard photons which come from hard processes. Usually hard photons also come from several sources in nucleus-nucleus collisions:direct photons from the initial hard scattering, such as:Compton scattering or annihilation process, the fragmentation photons produced by jet fragmentation, and photons converted from a fast jet, which happens when energetic partons traveling through the hot medium and interacting with the hot medium, this process can also produce hard photons. We are mainly interested in the hard photons in this thesis. In p+p collisions, the photon spectrum chiefly consists of direct photons and fragmentation photons. In A+A collisions, due to the effect of the medium, besides the fragmentation photons, we have to consider other photon sources:such as jet-photon conversion. So that the photon spectrum is complicated by the presence of a number of other photon sources during A+A collisions.
In this thesis, we study the influence of the final state energy loss in the production of the direct photons and estimate the transverse momentum dependence of the nuclear modification factor RAA-We use two different models for the bulk matter evolution in central Au+Au collisions at the RHIC energy:(1+1)d Bjorken model and (3+1) d ideal hydrodynamical model by Hirano to investigate the parton energy loss and discuss direct photon production coming from different sources. Our results show that at very low pΤ, thermal photon production is important in the photon production, and the thermal photon spectrum decrease very fast with pΤincrease; at high pΤregion, the direct photon production dominates photon production. The calculating results also show that the influence of energy loss is important for investigation the direct photon production at RHIC with (?)= 200 GeV, and jet-photon conversion plays an important role to explain experiment data in mid pr region besides the contribution from the direct photons and fragmentation photons.
Nuclear shadowing effects are investigated in productions of direct photons and neutral pions in heavy ion collisions at RHIC/LHC energy within a next-to-leading order perturbative QCD parton model. The transverse momentum dependence of the nuclear modification factors is presented in p+A and A+A collisions to distinguish different parameterizations for nuclear shadowing effects. Our numerical results show that in central A+A collisions the nuclear modification factor for direct photons is more sensitive to shadowing effects than the factor for pion hadrons, and it is a powerful observable to discriminate different parameterizations for parton distributions.
The nonlocal vacuum condensates of QCD describe the distributions of quarks and gluons in the nonperturbative QCD vacuum. Physically, this means that vacuum quarks and gluons have nonzero mean squared momentum, called virtuality. In this thesis we study the quark virtuality which is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The two vacuum condensates are obtained by solving Dyson-Schwinger equations of a fully dressed quark propagator with an effective gluon propagator. Using our calculated condensates, we obtain the virtuality of quarks in the QCD vacuum state. Our numerical predictions are consistent with other theoretical model calculations such as QCD sum rules, lattice QCD and instanton models.
通过多年的研究,人们相继提出了一些物理观测量,期望通过这些物理观测量来判定夸克胶子等离子体是否形成,例如：奇异粒子对产额的增长,J/ψ压低,集体流效应等等。其中,大横动量的光子产生被认为是研究QGP物质形态的理想指针信号。光子作为指针信号的优点在于：光子与其它粒子间的相互作用为电磁相互作用,电磁耦合常数(αe=1/(137))非常小,所以平均自由程比较大,产生的光子不与其它粒子发生强相互作用,能够离开碰撞区域被探测到,并携带QGP的热力学信息。
在核子-核子碰撞中产生的光子根据反应过程可分为：由软过程产生的软光子,即衰变光子；由硬过程产生的硬光子,包括直接光子(组分部分子直接通过湮灭过程或康普顿过程产生的光子)和碎裂光子。在核-核碰撞中,由于核介质效应,产生的光子根据反应过程可分为：由软过程产生的软光子,包括热光子和衰变光子：由硬过程产生的硬光子,包括直接光子和碎裂光子,以及2003年由R.J.Fries提出的一个硬过程产生的部分子与高温高密介质中的热部分子通过康普顿过程或正反夸克湮灭过程产生的光子,即喷注-光子转化(Jet-Photon conversion)。我们主要感兴趣的是由硬过程产生的光子。在p+p碰撞中,大横动量的光子谱主要由直接光子和碎裂光子组成。而在A+A碰撞中,强作用介质使得大横动量光子谱主要由直接光子、碎裂光子和喷注-光子转化产生。其中碎裂光子和喷注-光子转化都是由部分子喷注产生的,而部分子喷注在穿过高温高密介质时会发生多重散射诱发胶子辐射损失能量,因此和同一能量下的p+p碰撞产生的光子谱相比,A+A碰撞产生的光子谱将更复杂。这其中不但有初态的核效应,还有末态部分子喷注能量损失效应,以及由于强作用介质导致的其他光子产生,例如：喷注-光子转化。
在本文中,我们首先研究了RHIC高能核-核碰撞的直接光子产生。原来的高能核-核碰撞产生直接光子研究中,人们只计算到了光子产生的领头阶(LO),对于高阶修正的贡献是通过一个因子K人为引入的。我们通过直接计算核-核碰撞次领头阶(NLO)的贡献,考察了RHIC的Au+Au碰撞直接光子产生,避免了引入K因子计算高阶修正贡献的不确定性。在次领头阶(NLO)部分子模型的基础上,我们分别在(1+1)维Bjorken模型和(3+1)维理想流体力学模型下定量地研究了在RHIC能区对心度为0-10%的Au+Au碰撞的光子谱,并给出核修正因子RAA。通过对光子谱的研究,我们得到如下结果：热光子贡献主要在小pT区域,随着PT的增加热光子贡献迅速减小；在大PT区域,以直接光子的贡献为主,部分子的能量损失使得由碎裂光子和喷注-光子转化的贡献被大大压低。此外,我们还研究了核修正因子RAA。在横动量4GeV
木文的第二部分研究工作是在次领头阶(NLO)部分子模型的基础上,通过采用不同的初态核效应参数化形式,定量研究了在RHIC和LHC能区p十A和对心A+A碰撞中直接光子和中性π介子的核修正因子RpA和RAA。在考虑由于初态核介质效应引起部分子分布函数的修正时,我们采用了EKS,EPS,DS和HKN四种参数化形式。我们的研究结果表明：无论在RHIC还是LHC能区,对心A+A碰撞中直接光子的核修正因子RaγA是辨别现有的各种初态核效应参数的最有效工具。
本文的第三部分研究工作是基于“彩虹”近似,求解Dyson—Schwinger方程,研究QCD真空中夸克的虚度。QCD非定域的真空凝聚描述了在非微扰QCD真空中夸克和胶子的分布。物理上讲,这意味着真空中的夸克和胶子有非零的平均平方动量,此平均平方动量称之为夸克的虚度。夸克的虚度是由定域的夸克胶子的混合凝聚值与定域的夸克凝聚值之比决定的。我们基于有效的胶子传播子,在三组不同参数下(χ和△),求解夸克传播子的Dyson—Schwinger方程,计算了定域夸克真空凝聚值和定域夸克胶子混合真空凝聚值。利用计算的凝聚值,得到了QCD真空中夸克的虚度λq。我们的理论预言值与QCD求和规则、格点规范和瞬子模型等的理论计算结果一致。在具体计算中,我们发现对于有效的胶子传播子,(?)其第一项对夸克虚度的贡献是主要的,第二项的贡献可以忽略。
In 1970s, T.D. Lee and G.C.Wick predicted that a new state of matter—Quark Gluon Plasma(QGP) could be formed in relativistic heavy ion collisions. Since then, great progress has been made in the experimental and theoretical fields of heavy ion collisions. In 1980s, several experiments performed at AGS in the Brookheaven National Laboratory (BNL) in U.S. and at SPS in CERN in Europe. In the new century, the relativistic heavy ion collider (RHIC) in BNL with energy about 200 GeV has started taking data and obtained a lot of new results. Combining all of the experimental results, people believe that a strongly coupled QGP has been formed in heavy ion collisions. A giant accelerator known as Large Hadron Collider (LHC) at CERN has been in operation and will provide many new insights about the properties of QGP and the theory of strong interactions.
The QGP is a state of matter consisting of deconfined quarks and gluons. It is hypothesized to exist at high baryon densities and high temperature. These circumstances are available for experiments in heavy ion collisions, and even there the presence of the QGP cannot be measured directly. So far many signals have been proposed to probe the formation and the properties of QGP, such as:heavy quark enhancement, J/ψsuppression, collective flow, and so on. Among them, high pΤphoton production is a good signal to study the properties of QGP. Unlike hadrons, photons are gauge bosons in electromagnetic interaction in nature, (αe=(?)), they interact weakly with hadrons and their mean free path is large. As a result, once produced, the photons do not suffer further interaction with the medium and carry the information about the circumstances of their production to the detector.
In nucleon-nucleon collisions, photons can be categorized into the soft photons which come from soft processes, such as:decay photons, and the hard photons which come from hard pro-cesses, such as:direct photons and fragmentation photons. In nucleus-nucleus collisions, due to the effect of the medium, photons can be categorized into thermal photons which emitted from a thermalized plasma, decay photons which decay from the hadrons such as pions and etas, and hard photons which come from hard processes. Usually hard photons also come from several sources in nucleus-nucleus collisions:direct photons from the initial hard scattering, such as:Compton scattering or annihilation process, the fragmentation photons produced by jet fragmentation, and photons converted from a fast jet, which happens when energetic partons traveling through the hot medium and interacting with the hot medium, this process can also produce hard photons. We are mainly interested in the hard photons in this thesis. In p+p collisions, the photon spectrum chiefly consists of direct photons and fragmentation photons. In A+A collisions, due to the effect of the medium, besides the fragmentation photons, we have to consider other photon sources:such as jet-photon conversion. So that the photon spectrum is complicated by the presence of a number of other photon sources during A+A collisions.
In this thesis, we study the influence of the final state energy loss in the production of the direct photons and estimate the transverse momentum dependence of the nuclear modification factor RAA-We use two different models for the bulk matter evolution in central Au+Au collisions at the RHIC energy:(1+1)d Bjorken model and (3+1) d ideal hydrodynamical model by Hirano to investigate the parton energy loss and discuss direct photon production coming from different sources. Our results show that at very low pΤ, thermal photon production is important in the photon production, and the thermal photon spectrum decrease very fast with pΤincrease; at high pΤregion, the direct photon production dominates photon production. The calculating results also show that the influence of energy loss is important for investigation the direct photon production at RHIC with (?)= 200 GeV, and jet-photon conversion plays an important role to explain experiment data in mid pr region besides the contribution from the direct photons and fragmentation photons.
Nuclear shadowing effects are investigated in productions of direct photons and neutral pions in heavy ion collisions at RHIC/LHC energy within a next-to-leading order perturbative QCD parton model. The transverse momentum dependence of the nuclear modification factors is presented in p+A and A+A collisions to distinguish different parameterizations for nuclear shadowing effects. Our numerical results show that in central A+A collisions the nuclear modification factor for direct photons is more sensitive to shadowing effects than the factor for pion hadrons, and it is a powerful observable to discriminate different parameterizations for parton distributions.
The nonlocal vacuum condensates of QCD describe the distributions of quarks and gluons in the nonperturbative QCD vacuum. Physically, this means that vacuum quarks and gluons have nonzero mean squared momentum, called virtuality. In this thesis we study the quark virtuality which is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The two vacuum condensates are obtained by solving Dyson-Schwinger equations of a fully dressed quark propagator with an effective gluon propagator. Using our calculated condensates, we obtain the virtuality of quarks in the QCD vacuum state. Our numerical predictions are consistent with other theoretical model calculations such as QCD sum rules, lattice QCD and instanton models.
引文
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