介质中喷注演化的研究
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摘要
量子色动力学(QCD)是描述强相互作用的非阿贝尔规范场理论。它有两个基本性质：渐进自由和夸克禁闭。渐进自由的性质让我们可以在大动量或者极短程相互作用过程中使用微扰QCD进行计算。而夸克禁闭的性质让我们无法观测到自由夸克的存在。
然而,量子色动力学预言在高温高密度条件下夸克胶子可以处于解禁闭相,在一个比强子尺度大的时空范围内自由存在。高温高密可以达到相变所需的条件,使强子的外壳不复存在,夸克和胶子形成一种新的物质形态。这种新物质态后来被叫做夸克胶子等离子体(QGP)。
理论上,这种高能量密度的物质形态可以用高能重离子碰撞(即核-核碰撞)来实现。质心能量足够高的相对论重离子碰撞可以提供QGP形成所需要的高温和高密度。过去几十年里,美国布鲁海文国家实验室(BNL)和欧洲的核子研究中心(CERN)进行了大量的高能重离子碰撞实验,产生了丰富的实验结果,有迹象表明夸克胶子等离子体已经在实验中产生。
高能重离子实验中我们实际能观测到的只有末态强子,如何从末态强子中分离出QGP存在的信息,是当前高能重离子物理的热门课题。我们知道,随着碰撞能量的提高,硬过程对截面的贡献也越来越大。在RHIC和LHC的能量范围内,硬过程已经变得非常重要。由硬过程产生的大横动量喷注可以作为探测QGP存在信号的硬探针。
理论预言硬过程中被散射的大横动量部分子在穿越强相互作用物质时,会因为多重散射而损失能量。导致我们在实验上看到的喷注淬火(Jet Quenching)现象。大横动量部分子的能量损失对它所穿过的介质的性质非常敏感。所以硬探针的能量损失就成为探测QGP形成的重要信号。由Gyulassy和X.N.Wang提出的模型(GW模型)认为部分子穿过热的部分子介质时的能量损失是由于多重散射而诱发辐射出的胶子带走的,且有效能量损失正比于介质中胶子密度。GW模型指出和弹性碰撞的能量损失相比,非弹性碰撞能量损失的贡献是主要的。另外,部分子穿过冷的核物质时也应该有类似的能量损失效应。计算和比较冷热两种核物质环境下部分子的能量损失的不同之处,可以给我们更多的关于核物质性质的信息。
然而,由于量子色动力学中部分子的能量损失不是可以直接测量的。而且传统上喷注的定义是指相空间中的一簇强子,它的整体能量不会因为介质诱发辐射而改变。改变的只是喷注中这一簇强子的能量分布。所以由于多重散射而诱发的胶子辐射会导致初始部分子碎裂函数的修正,从而给出部分子的能量损失。
在深度非弹性散射中,被硬过程激发的夸克穿过冷核介质时,末态辐射将给出类似于真空中依赖于标度且满足DGLAP演化方程的碎裂函数。而与核物质多重散射而诱发的胶子辐射会在演化方程中增加额外的项。从而导致对夸克的碎裂函数和其满足的DGLAP演化方程的介质修正。
DGLAP演化方程中不仅包括夸克喷注的介质修正的碎裂函数,还应该包括与胶子喷注相关的碎裂函数的修正项。因为胶子喷注在穿过介质的时候也会发生同样的多重散射并诱发额外的胶子辐射,并进而修正胶子的碎裂函数。而且胶子喷注除了诱发的胶子辐射之外,还应该有额外的夸克-反夸克对产生的项。基于同样的考虑到多重部分子散射的广义的因子化框架内,关于夸克-夸克(反夸克)的双重散射的研究让我们可以把这一部分的贡献也包括进来。本文第一部分内容中,我们将这些介质修正项全都包括进演化方程中,就可以得到完整的夸克胶子互相耦合的修正的演化方程。这样就可以得到夸克和胶子互相耦合的完整的介质修正DGLAP演化方程(mDGLAP)。而且我们采用基于Runge-Kutta迭代方法的数值解法,可以得到给定初始条件的mDGLAP方程演化到任意能量标度下的所有部分子的修正碎裂函数。这样我们就可以计算任意核环境下部分子的能量损失,可以对核介质中部分子演化的行为进行系统性研究。
本文第二部分内容主要关注在理想的“方块”介质中喷注的演化行为。为了能够明确考察mDGLAP方程演化得到的修正的碎裂函数是如何依赖于初始部分子的能量E、演化标度Q2、核介质的长度L和喷注输运参数q(也就是核介质中的胶子密度),我们假设了一种具有有限长度、密度均匀的理想核环境,称之为“方块”核环境(brick)。在“方块”核环境中,我们用特殊的δ-函数δ(1-z)作为mDGLAP演化方程中单个部分子的初始条件,考察了在初始部分子形成的簇射中末态部分子的演化和分布。另外在介质诱发的胶子辐射和夸克对产生过程中,如何定义能量损失是一个比较困难的事情。我们的工作中将能量损失定义为初始部分子由介质诱发辐射出的胶子和夸克-反夸克对所带走的能量分数,从而计算了由mDGLAP方程演化得到的能量损失,并跟传统的胶子诱发辐射导致的能量损失作了比较。我们还在核环境中引入真实的部分子碎裂函数作为初始条件,考察了不同核环境参数下演化得到的碎裂函数的演化行为,并由此得到核修正因子对不同核环境参数的依赖关系。
本文第三部分内容将重点研究真实的核环境下喷注演化的行为。首先,我们考察了电子-核的深度非弹性散射半单举实验。应用Woods-Saxon模型描写核中的核子分布,计算不同原子量的冷核环境下由mDGLAP演化方程计算得到冷核中的介质修正的碎裂函数,并且计算出相应的核修正因子。并且我们进一步确认了在初始能量标度下,介质中喷注演化的初始条件与真空中的初始条件是有区别的这一假设。我们将计算结果与实验数据作比较,从中抽取出对应于冷核介质的喷注输运参数。另外,我们还将这—计算方法应用到高能重离子碰撞实验中,运用实际物理过程中的核几何函数,由mDGLAP方程演化得到对应于RHIC能级下的介质修正因子RAA。我们将计算结果跟实验数据比较,得到RHIC能级下QGP中的喷注输运参数。通过计算我们得到对应于冷热两种核物质中的胶子密度信息。我们的计算对于确认高能重离子反应中QGP的产生以及研究QGP物质的状态性质提供了有效方法。
Quantum chromodynamics (QCD) is the field theory based on a non-abelian gauge group SU(3). At present QCD is well-established as the theory of strong interaction. QCD has two elementary and important properties: asymptotical freedom and confinement. The first property allows us using perturbative expansion to deal with the high energy transfer processes. The latter property is the origin why we cannot observe free quarks or gluons.
However, theoretical calculation of QCD predict there exist a new state of matter in high temperature or high baryon density which can be reached in high energy heavy-ion collisions. In this new matter phase, quarks and gluons can be de-confinement in a space much larger than hadrons. We call it as Quark-Gluon-Plasma (QGP).
To tell whether there is QGP formation we should have some measure-ments which are able to distinguish between the QGP phase and normal hadronic phase. We call these measurements as QGP signature. One of the QGP signature found in high energy heavy-ion collisions is the Jet Quench-ing.
Jet quenching or the suppression of large transverse momentum spec-tra can be used as an effective probe of the properties of dense medium created in high energy heavy-ion collisions. Because of multiple scattering and induced gluon bremsstrahlung, an energetic parton propagating in dense medium will lose a significant amount of energy and therefore soften its final fragmentation functions. These modified fragmentation functions will lead to the suppression of large transverse momentum single hadron spectra, photon-hadron correlations both away-side and same-side dihadron correlations in high-energy heavy-ion collisions.
Such proposed phenomena have indeed been observed in experiments at the Relativistic Heavy-ion Collider (RHIC). Phenomenological studies of the observed jet quenching phenomena at RHIC indicate a scenario of strong interaction between energetic partons and the hot medium with an extremely high initial parton density. The same phenomena are also predicted in deeply inelastic scattering (DIS) off large nuclei when the struck quark propagates through the target nuclei though the extracted parton density in cold nuclei is much smaller than that in the hot matter produced in the central Au+Au collisions at RHIC.
In the first part of this dissertation, within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross section of deeply inelastic scattering off a large nucleus, multiple parton scattering leads to an effective medium-modified fragmentation function and the correspond-ing medium-modified DGLAP evolution equations. We extend the study to include gluon multiple scattering and induced quark-antiquark production via gluon fusion.
In the second part of this dissertation, we numerically solve these medium-modified DGLAP (mDGLAP) evolution equations and study the scale (Q2), energy (E), length (L) and jet transport parameter (q) dependence of the modified fragmentation functions for a jet propagating in a uniform medium with finite length (a "brick" problem). We also discuss the concept of parton energy loss within such mDGLAP evolution equations and its connection to the modified fragmentation functions.
In the third part of this dissertation, we concentrate on the jet evolution in realistic nuclear medium. With a realistic Wood-Saxon nuclear geometry, we calculate the modified fragmentation functions and compare to exper-imental data of DIS off large nuclei. And we extracted the jet transport parameter at the center of a large nucleus via compared our calculations with the HERMES experimental data for three different nucleus. Further-more, we calculate the modification factor RAA for QGP produced in high energy nuclear collisions. We extracted the jet transport parameter from comparing with RHIC data also.
然而,量子色动力学预言在高温高密度条件下夸克胶子可以处于解禁闭相,在一个比强子尺度大的时空范围内自由存在。高温高密可以达到相变所需的条件,使强子的外壳不复存在,夸克和胶子形成一种新的物质形态。这种新物质态后来被叫做夸克胶子等离子体(QGP)。
理论上,这种高能量密度的物质形态可以用高能重离子碰撞(即核-核碰撞)来实现。质心能量足够高的相对论重离子碰撞可以提供QGP形成所需要的高温和高密度。过去几十年里,美国布鲁海文国家实验室(BNL)和欧洲的核子研究中心(CERN)进行了大量的高能重离子碰撞实验,产生了丰富的实验结果,有迹象表明夸克胶子等离子体已经在实验中产生。
高能重离子实验中我们实际能观测到的只有末态强子,如何从末态强子中分离出QGP存在的信息,是当前高能重离子物理的热门课题。我们知道,随着碰撞能量的提高,硬过程对截面的贡献也越来越大。在RHIC和LHC的能量范围内,硬过程已经变得非常重要。由硬过程产生的大横动量喷注可以作为探测QGP存在信号的硬探针。
理论预言硬过程中被散射的大横动量部分子在穿越强相互作用物质时,会因为多重散射而损失能量。导致我们在实验上看到的喷注淬火(Jet Quenching)现象。大横动量部分子的能量损失对它所穿过的介质的性质非常敏感。所以硬探针的能量损失就成为探测QGP形成的重要信号。由Gyulassy和X.N.Wang提出的模型(GW模型)认为部分子穿过热的部分子介质时的能量损失是由于多重散射而诱发辐射出的胶子带走的,且有效能量损失正比于介质中胶子密度。GW模型指出和弹性碰撞的能量损失相比,非弹性碰撞能量损失的贡献是主要的。另外,部分子穿过冷的核物质时也应该有类似的能量损失效应。计算和比较冷热两种核物质环境下部分子的能量损失的不同之处,可以给我们更多的关于核物质性质的信息。
然而,由于量子色动力学中部分子的能量损失不是可以直接测量的。而且传统上喷注的定义是指相空间中的一簇强子,它的整体能量不会因为介质诱发辐射而改变。改变的只是喷注中这一簇强子的能量分布。所以由于多重散射而诱发的胶子辐射会导致初始部分子碎裂函数的修正,从而给出部分子的能量损失。
在深度非弹性散射中,被硬过程激发的夸克穿过冷核介质时,末态辐射将给出类似于真空中依赖于标度且满足DGLAP演化方程的碎裂函数。而与核物质多重散射而诱发的胶子辐射会在演化方程中增加额外的项。从而导致对夸克的碎裂函数和其满足的DGLAP演化方程的介质修正。
DGLAP演化方程中不仅包括夸克喷注的介质修正的碎裂函数,还应该包括与胶子喷注相关的碎裂函数的修正项。因为胶子喷注在穿过介质的时候也会发生同样的多重散射并诱发额外的胶子辐射,并进而修正胶子的碎裂函数。而且胶子喷注除了诱发的胶子辐射之外,还应该有额外的夸克-反夸克对产生的项。基于同样的考虑到多重部分子散射的广义的因子化框架内,关于夸克-夸克(反夸克)的双重散射的研究让我们可以把这一部分的贡献也包括进来。本文第一部分内容中,我们将这些介质修正项全都包括进演化方程中,就可以得到完整的夸克胶子互相耦合的修正的演化方程。这样就可以得到夸克和胶子互相耦合的完整的介质修正DGLAP演化方程(mDGLAP)。而且我们采用基于Runge-Kutta迭代方法的数值解法,可以得到给定初始条件的mDGLAP方程演化到任意能量标度下的所有部分子的修正碎裂函数。这样我们就可以计算任意核环境下部分子的能量损失,可以对核介质中部分子演化的行为进行系统性研究。
本文第二部分内容主要关注在理想的“方块”介质中喷注的演化行为。为了能够明确考察mDGLAP方程演化得到的修正的碎裂函数是如何依赖于初始部分子的能量E、演化标度Q2、核介质的长度L和喷注输运参数q(也就是核介质中的胶子密度),我们假设了一种具有有限长度、密度均匀的理想核环境,称之为“方块”核环境(brick)。在“方块”核环境中,我们用特殊的δ-函数δ(1-z)作为mDGLAP演化方程中单个部分子的初始条件,考察了在初始部分子形成的簇射中末态部分子的演化和分布。另外在介质诱发的胶子辐射和夸克对产生过程中,如何定义能量损失是一个比较困难的事情。我们的工作中将能量损失定义为初始部分子由介质诱发辐射出的胶子和夸克-反夸克对所带走的能量分数,从而计算了由mDGLAP方程演化得到的能量损失,并跟传统的胶子诱发辐射导致的能量损失作了比较。我们还在核环境中引入真实的部分子碎裂函数作为初始条件,考察了不同核环境参数下演化得到的碎裂函数的演化行为,并由此得到核修正因子对不同核环境参数的依赖关系。
本文第三部分内容将重点研究真实的核环境下喷注演化的行为。首先,我们考察了电子-核的深度非弹性散射半单举实验。应用Woods-Saxon模型描写核中的核子分布,计算不同原子量的冷核环境下由mDGLAP演化方程计算得到冷核中的介质修正的碎裂函数,并且计算出相应的核修正因子。并且我们进一步确认了在初始能量标度下,介质中喷注演化的初始条件与真空中的初始条件是有区别的这一假设。我们将计算结果与实验数据作比较,从中抽取出对应于冷核介质的喷注输运参数。另外,我们还将这—计算方法应用到高能重离子碰撞实验中,运用实际物理过程中的核几何函数,由mDGLAP方程演化得到对应于RHIC能级下的介质修正因子RAA。我们将计算结果跟实验数据比较,得到RHIC能级下QGP中的喷注输运参数。通过计算我们得到对应于冷热两种核物质中的胶子密度信息。我们的计算对于确认高能重离子反应中QGP的产生以及研究QGP物质的状态性质提供了有效方法。
Quantum chromodynamics (QCD) is the field theory based on a non-abelian gauge group SU(3). At present QCD is well-established as the theory of strong interaction. QCD has two elementary and important properties: asymptotical freedom and confinement. The first property allows us using perturbative expansion to deal with the high energy transfer processes. The latter property is the origin why we cannot observe free quarks or gluons.
However, theoretical calculation of QCD predict there exist a new state of matter in high temperature or high baryon density which can be reached in high energy heavy-ion collisions. In this new matter phase, quarks and gluons can be de-confinement in a space much larger than hadrons. We call it as Quark-Gluon-Plasma (QGP).
To tell whether there is QGP formation we should have some measure-ments which are able to distinguish between the QGP phase and normal hadronic phase. We call these measurements as QGP signature. One of the QGP signature found in high energy heavy-ion collisions is the Jet Quench-ing.
Jet quenching or the suppression of large transverse momentum spec-tra can be used as an effective probe of the properties of dense medium created in high energy heavy-ion collisions. Because of multiple scattering and induced gluon bremsstrahlung, an energetic parton propagating in dense medium will lose a significant amount of energy and therefore soften its final fragmentation functions. These modified fragmentation functions will lead to the suppression of large transverse momentum single hadron spectra, photon-hadron correlations both away-side and same-side dihadron correlations in high-energy heavy-ion collisions.
Such proposed phenomena have indeed been observed in experiments at the Relativistic Heavy-ion Collider (RHIC). Phenomenological studies of the observed jet quenching phenomena at RHIC indicate a scenario of strong interaction between energetic partons and the hot medium with an extremely high initial parton density. The same phenomena are also predicted in deeply inelastic scattering (DIS) off large nuclei when the struck quark propagates through the target nuclei though the extracted parton density in cold nuclei is much smaller than that in the hot matter produced in the central Au+Au collisions at RHIC.
In the first part of this dissertation, within the framework of generalized factorization of higher-twist contributions to semi-inclusive cross section of deeply inelastic scattering off a large nucleus, multiple parton scattering leads to an effective medium-modified fragmentation function and the correspond-ing medium-modified DGLAP evolution equations. We extend the study to include gluon multiple scattering and induced quark-antiquark production via gluon fusion.
In the second part of this dissertation, we numerically solve these medium-modified DGLAP (mDGLAP) evolution equations and study the scale (Q2), energy (E), length (L) and jet transport parameter (q) dependence of the modified fragmentation functions for a jet propagating in a uniform medium with finite length (a "brick" problem). We also discuss the concept of parton energy loss within such mDGLAP evolution equations and its connection to the modified fragmentation functions.
In the third part of this dissertation, we concentrate on the jet evolution in realistic nuclear medium. With a realistic Wood-Saxon nuclear geometry, we calculate the modified fragmentation functions and compare to exper-imental data of DIS off large nuclei. And we extracted the jet transport parameter at the center of a large nucleus via compared our calculations with the HERMES experimental data for three different nucleus. Further-more, we calculate the modification factor RAA for QGP produced in high energy nuclear collisions. We extracted the jet transport parameter from comparing with RHIC data also.
引文
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