RHIC和LHC能量下大横动量强子谱的压低
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摘要
夸克胶子等离子体(QGP)是量子色动力学(QCD)预言的强子物质在高温高密时的一种状态,这个时候强子物质中被禁闭的夸克可以以夸克自由度存在。QGP被认为是宇宙大爆炸之后很短时间内的物质状态,因而研究QGP对更好地理解宇宙的演化和量子色动力学本身都是很重要的。现在位于美国布鲁克海文国家实验室的相对论重离子对撞机(RHIC)以及欧洲核子中心的大型强子对撞机(LHC)上的重离子对撞实验被认为已经产生了QGP物质。实验上探测QGP的可观测量主要是小横动量强子的集体流行为和大横动量强子谱的压低。后者被称为喷注淬火,本文将对它进行系统的研究。
在重离子碰撞过程中,硬散射产生的大横动量的部分子在穿过周围的QGP时会与QGP中的物质相互作用而损失能量,造成部分子碎裂产生的大横动量强子的产额降低。在微扰QCD的计算中,强子的横动量谱可以通过初态部分子分布函数、两部分子的散射截面和末态部分子碎裂函数的卷积得到。由于喷注淬火的主要原因是末态部分子与介质的相互作用,因此我们可以引入介质修正的碎裂函数来包含相互作用的信息,以此计算被介质修正的强子谱。
在电子与原子核的深度非弹散射过程中,被虚光子击出的部分子在穿过周围的冷核介质时也会损失能量造成强子谱的压低。在高扭度框架下,末态部分子与介质的相互作用诱发的胶子辐射可以被视为对真空中劈裂函数的修正。介质修正的碎裂函数可以通过求解介质修正的DGLAP(mDGLAP)演化方程得到。mDGLAP演化方程是在电子与原子核的深度非弹散射过程中被推导出来的,文献[45]的作者们通过严格求解nDGLAP演化方程并计算核修正因子可以解释HERMES实验组的数据。
本文继续文献[45]的工作,把理论框架从深度非弹过程推广到重离子碰撞过程。这个时候我们认识到解：nDGLAP演化方程时,作为输入的初始条件是非常重要的。把文献[45]中用到的简单的初始条件使用到重离子碰撞过程中是不能解释实验数据的。
借鉴其他理论组用辐射胶子谱得到的淬火因子跟真空中碎裂函数卷积得到介质修正的碎裂函数的方法。我们在高扭度框架下也计算了部分子辐射的胶子谱和淬火因子,但我们只用它来得到解：nDGLAP演化方程需要的初始条件。用这样的初始条件得到的碎裂函数,我们可以同时描述HERMES上的深度非弹实验数据和RHIC上的重离子碰撞实验数据。
LHC上的重离子碰撞实验提供了更高能量范围的实验数据,也对理论提出了更严格的要求。好多理论组发现,把RHIC能量的框架推广的LHC能量下会高估大横动量处强子谱的压低。后来大家认识到,如果让LHC能量下的耦合常数变小,可以解决这个问题。我们一开始也遇到了这个问题,调节耦合常数之后确实可以同时描述RHIC和LHC上的实验数据。
我们还提出了另一种机制来解释它。由于高扭度贡献是被标度Q2的倒数1/Q2压低的,因此高扭度修正主要来自于Q2较小时的贡献。能量大的部分子,它的虚度演化到给定Q2比能量小的部分子需要的时间更长。也就是能量大的部分子在虚度处于给定Q2时处于介质更晚期的更外围,由于QGP随时间非常快地冷却稀释,因此能量大的部分子在给定Q2时与介质的相互作用要少。为了获得部分子虚度随时空的演化信息,本文仿照PYTHIA中部分子在真空中簇射的算法,建立了部分子在介质中簇射的模型。这个信息可以修正我们对介质诱发的劈裂函数的计算,帮助我们解释LHC上的实验数据。
The Quantum Chromodynamics (QCD) predicts the existence of Quark-gluon plasmas (QGP), which is a new phase of hadron matter at high temperature and high density where the quark degrees of freedom normally confined within hadrons are lib-erated. QGP is thought to exist in the very early universe after the Big Bang. Thus studying the properties of QGP is very important for our deeper understanding of the evolution of universe as well as the physics of QCD. Now it's believed that QGP has been created in the experiments of heavy ion collisions in RHIC (Relativistic Heavy-Ion Collider) at BNL and LHC (Large Hadron Collider) at CERN. There are mainly two kinds of observables to study the matter created in heavy ion collisions, the col-lective flow of soft hadrons and the suppression of large transverse momentum spectra of hard hadrons (jet quenching). This thesis focuses on the later one.
In heavy-ion collisions, high pt parton produced by hard scattering will pene-trate the formed QGP and lose a large amount of energy through multiple scatterings with thermal partons in QGP, which results in the suppression of large transverse mo-mentum spectra of hadrons. In perturbative QCD the transverse momentum spectra of hadrons can be calculated by the convolution of distribution functions of colliding partons, cross-section of two partons and the fragmentation function which represents the probability of the final parton fragmentates into hadrons. Owing to the fact that jet quenching mainly stems from final interactions, it is natural to introduce the modified fragmentation functions (mFF) to express the softening of the hadron spectra.
In the process of deep inelastic scattering (DIS) of a large nucleus, the outgoing parton struck by the virtual photon will also lose its energy when passing though the remainder cold nuclear matter. In higher-twist approach, the interactions of the hard parton with the medium will induce additional gluon bremsstrahlung which will mod-ify the splitting functions in vacuum. Then mFF can be solved out by the evolution of the modified DGLAP (mDGLAP) equations which were derived in DIS. In Ref.[45] the mDGLAP equations were solved numerically for the first time and the application in DIS exhibits its validity in describing the experimental data at HERMES.
In this thesis we extend the framework form DIS to heavy-ion collisions. We realize that the initial condition which is the input to solve mDGLAP equations is very important. If we use the naive initial condition in Ref.[45] we can't explain the experimental data at RHIC.
Other groups don't obtain mFF by solving mDGLAP equations. They get mFF by the convolution of fragmentation functions in vacuum with the quenching weight which is calculated by the induced gluon spectra. We can also calculate induced gluon spectra and quenching weight in higher-twist approach. Using the initial condition by convolution we can describe the experimental data in DIS at HERMES and heavy-ion collisions at RHIC.
After the data at LHC released, people find there are some difficulties to fit the data well if we simply extend the calculation at RHIC to LHC. Usually, we will over-rate the suppression at large pT. It's realized latter that a reduced coupling constant at LHC can explain the problem. After we using a running coupling constant instead of a fixed one, we can indeed fit the data at RHIC and LHC simultaneously.
Moreover, we find a new mechanism which can settle the problem as well. The higher-twist modification mainly comes from the contribution of small Q2because the higher-twist term is suppressed by1/Q2, where the Q2in mDGLAP equations can be served as the virtuality of the final parton. Parton with more energy needs more time to lose its virtuality to Q2than the parton with less energy. That means at a given Q2the parton with more energy locates at the later period of QGP. Because the QGP dilutes quickly, the parton with more energy will have less interactions with the medium. We develop a simple model of parton shower in medium base on the tactics of PYTHIA to get the information of the virtuality of the final parton on its path. This information can modify our calculations on medium induced splitting function and help us to explain the experimental data at LHC.
在重离子碰撞过程中,硬散射产生的大横动量的部分子在穿过周围的QGP时会与QGP中的物质相互作用而损失能量,造成部分子碎裂产生的大横动量强子的产额降低。在微扰QCD的计算中,强子的横动量谱可以通过初态部分子分布函数、两部分子的散射截面和末态部分子碎裂函数的卷积得到。由于喷注淬火的主要原因是末态部分子与介质的相互作用,因此我们可以引入介质修正的碎裂函数来包含相互作用的信息,以此计算被介质修正的强子谱。
在电子与原子核的深度非弹散射过程中,被虚光子击出的部分子在穿过周围的冷核介质时也会损失能量造成强子谱的压低。在高扭度框架下,末态部分子与介质的相互作用诱发的胶子辐射可以被视为对真空中劈裂函数的修正。介质修正的碎裂函数可以通过求解介质修正的DGLAP(mDGLAP)演化方程得到。mDGLAP演化方程是在电子与原子核的深度非弹散射过程中被推导出来的,文献[45]的作者们通过严格求解nDGLAP演化方程并计算核修正因子可以解释HERMES实验组的数据。
本文继续文献[45]的工作,把理论框架从深度非弹过程推广到重离子碰撞过程。这个时候我们认识到解：nDGLAP演化方程时,作为输入的初始条件是非常重要的。把文献[45]中用到的简单的初始条件使用到重离子碰撞过程中是不能解释实验数据的。
借鉴其他理论组用辐射胶子谱得到的淬火因子跟真空中碎裂函数卷积得到介质修正的碎裂函数的方法。我们在高扭度框架下也计算了部分子辐射的胶子谱和淬火因子,但我们只用它来得到解：nDGLAP演化方程需要的初始条件。用这样的初始条件得到的碎裂函数,我们可以同时描述HERMES上的深度非弹实验数据和RHIC上的重离子碰撞实验数据。
LHC上的重离子碰撞实验提供了更高能量范围的实验数据,也对理论提出了更严格的要求。好多理论组发现,把RHIC能量的框架推广的LHC能量下会高估大横动量处强子谱的压低。后来大家认识到,如果让LHC能量下的耦合常数变小,可以解决这个问题。我们一开始也遇到了这个问题,调节耦合常数之后确实可以同时描述RHIC和LHC上的实验数据。
我们还提出了另一种机制来解释它。由于高扭度贡献是被标度Q2的倒数1/Q2压低的,因此高扭度修正主要来自于Q2较小时的贡献。能量大的部分子,它的虚度演化到给定Q2比能量小的部分子需要的时间更长。也就是能量大的部分子在虚度处于给定Q2时处于介质更晚期的更外围,由于QGP随时间非常快地冷却稀释,因此能量大的部分子在给定Q2时与介质的相互作用要少。为了获得部分子虚度随时空的演化信息,本文仿照PYTHIA中部分子在真空中簇射的算法,建立了部分子在介质中簇射的模型。这个信息可以修正我们对介质诱发的劈裂函数的计算,帮助我们解释LHC上的实验数据。
The Quantum Chromodynamics (QCD) predicts the existence of Quark-gluon plasmas (QGP), which is a new phase of hadron matter at high temperature and high density where the quark degrees of freedom normally confined within hadrons are lib-erated. QGP is thought to exist in the very early universe after the Big Bang. Thus studying the properties of QGP is very important for our deeper understanding of the evolution of universe as well as the physics of QCD. Now it's believed that QGP has been created in the experiments of heavy ion collisions in RHIC (Relativistic Heavy-Ion Collider) at BNL and LHC (Large Hadron Collider) at CERN. There are mainly two kinds of observables to study the matter created in heavy ion collisions, the col-lective flow of soft hadrons and the suppression of large transverse momentum spectra of hard hadrons (jet quenching). This thesis focuses on the later one.
In heavy-ion collisions, high pt parton produced by hard scattering will pene-trate the formed QGP and lose a large amount of energy through multiple scatterings with thermal partons in QGP, which results in the suppression of large transverse mo-mentum spectra of hadrons. In perturbative QCD the transverse momentum spectra of hadrons can be calculated by the convolution of distribution functions of colliding partons, cross-section of two partons and the fragmentation function which represents the probability of the final parton fragmentates into hadrons. Owing to the fact that jet quenching mainly stems from final interactions, it is natural to introduce the modified fragmentation functions (mFF) to express the softening of the hadron spectra.
In the process of deep inelastic scattering (DIS) of a large nucleus, the outgoing parton struck by the virtual photon will also lose its energy when passing though the remainder cold nuclear matter. In higher-twist approach, the interactions of the hard parton with the medium will induce additional gluon bremsstrahlung which will mod-ify the splitting functions in vacuum. Then mFF can be solved out by the evolution of the modified DGLAP (mDGLAP) equations which were derived in DIS. In Ref.[45] the mDGLAP equations were solved numerically for the first time and the application in DIS exhibits its validity in describing the experimental data at HERMES.
In this thesis we extend the framework form DIS to heavy-ion collisions. We realize that the initial condition which is the input to solve mDGLAP equations is very important. If we use the naive initial condition in Ref.[45] we can't explain the experimental data at RHIC.
Other groups don't obtain mFF by solving mDGLAP equations. They get mFF by the convolution of fragmentation functions in vacuum with the quenching weight which is calculated by the induced gluon spectra. We can also calculate induced gluon spectra and quenching weight in higher-twist approach. Using the initial condition by convolution we can describe the experimental data in DIS at HERMES and heavy-ion collisions at RHIC.
After the data at LHC released, people find there are some difficulties to fit the data well if we simply extend the calculation at RHIC to LHC. Usually, we will over-rate the suppression at large pT. It's realized latter that a reduced coupling constant at LHC can explain the problem. After we using a running coupling constant instead of a fixed one, we can indeed fit the data at RHIC and LHC simultaneously.
Moreover, we find a new mechanism which can settle the problem as well. The higher-twist modification mainly comes from the contribution of small Q2because the higher-twist term is suppressed by1/Q2, where the Q2in mDGLAP equations can be served as the virtuality of the final parton. Parton with more energy needs more time to lose its virtuality to Q2than the parton with less energy. That means at a given Q2the parton with more energy locates at the later period of QGP. Because the QGP dilutes quickly, the parton with more energy will have less interactions with the medium. We develop a simple model of parton shower in medium base on the tactics of PYTHIA to get the information of the virtuality of the final parton on its path. This information can modify our calculations on medium induced splitting function and help us to explain the experimental data at LHC.
引文
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