Parton branching and medium-induced radiation in a strongly coupled plasma
Edmond Iancu
我审查的部分子图片出现在强耦合的规范/重力的二重性及其后果的能量损失和动量加宽的重夸克移动通过强耦合等离子体。
I review the parton picture at strong coupling emerging from the gauge/gravity duality together with its consequences for the energy loss and momentum broadening of a heavy quark moving through a strongly coupled plasma.
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We present a solution of the DGLAP evolution equations, written in terms of Sudakov form factors to describe the branching and no-branching probabilities, using a parton branching Monte Carlo method. We demonstrate numerically that this method reproduces the semi-analytical solutions. We show how this method can be used to determine Transverse Momentum Dependent (TMD) parton distribution functions, in addition to the usual integrated parton distributions functions. We discuss numerical effects of the boundary of soft gluon resolution scale parameter on the resulting parton distribution functio…
We briefly illustrate recent developments in the parton branching formulation of TMD evolution and their impact on precision measurements in high-energy hadronic collisions.
We review the current status of collinear and Transverse Momentum Dependent densities based on the Parton Branching method. We investigate the performance of the PB-TMD evolution as well as PB-TMD parton shower with different configurations of the hard process in the four- and five-flavour schemes.
Off-shell, transverse-momentum dependent splitting functions can be defined from the high-energy limit of partonic decay amplitudes. Based on these splitting functions, we construct Sudakov form factors and formulate a new parton branching algorithm. We present a first Monte Carlo implementation of the algorithm. We use the numerical results to verify explicitly momentum sum rules for TMD parton distributions.
Parton Branching in Color Mutation Model
对程函色突变分支模型中强子碰撞中的软产生问题进行了改进，改进了初始部分子分布的处理方法。部分子的毛茸茸的分支被认为是描述软相互作用中部分子再生的非微扰过程的一种手段。对于<n>q=2，.，所有矩和$C_q$的值5，以及它们的能量依赖性可以通过仅使用两个参数来正确地确定。
We present a determination of parton densities at NLO obtained with the Parton Branching method using precision measurements of deep inelastic scattering cross sections at HERA. The two sets of parton densities shown in this work are obtained with the same angular angular ordering condition for the evolution scale and they differ in the chosen scale for the strong coupling evaluation, for which we consider two scenarios: the evolution scale, and the transverse momentum qT from the angular ordering prescription. The transverse momentum dependent densities obtained with the Parton Branching meth…
I report on precision comparisons of theoretical predictions for Drell-Yan (DY) transverse momentum spectra from two approaches: the analytical resummation approach based on Collins-Soper-Sterman (CSS) formalism and the parton branching (PB) approach to the evolution of transverse momentum dependent (TMD) parton distributions.
We explore the possibility to include small-$x$ dynamics effects in the parton branching (PB) approach to transverse momentum dependent (TMD) parton distribution functions. To this end, we first revisit the PB method at leading order, presenting a new fit to inclusive-DIS precision data, and performing a numerical study of the dynamic soft-gluon resolution scale. Next we investigate the effects of modified CCFM kernels, including both Sudakov and non-Sudakov form factors.
The Parton Branching (PB) Method describes the evolution of transverse momentum dependent parton densities (TMDs). The obtained TMDs can be used in Monte Carlo generators to describe physical observables. We give an overview of recent developments, in particular the new application of PB TMDs in Drell-Yan + jets production, the four-flavor and five-flavor schemes for heavy quark contributions, and the inclusion of QED corrections in the PB evolution.
The Parton Branching (PB) approach describes the evolution of transverse momentum dependent (TMD) parton densities. We propose to extend the PB method by including TMD splitting functions, instead of the DGLAP splitting functions which assume strong ordering in transverse momentum. We present the evolution equations and their numerical solution, which is the first Monte Carlo implementation including TMD splitting functions.
Calculations of Drell-Yan (DY) production at next-to-leading (NLO) order have been combined with Transverse Momentum Dependent (TMD) distributions obtained with the Parton Branching (PB). The predictions show a remarkable agreement with DY measurement from E605 experiment, consistent with previous results we obtained for R209, PHENIX, CMS and ATLAS experiments. We also present predictions for Z+jet measurements showing the importance of TMD parton shower contributions to the jet multiplicity. We show that PB-TMD parton density and the corresponding PB-TMD parton shower can be combined with lea…
Parton branching methods underlie the Monte Carlo (MC) generators, being therefore of key importance for obtaining high energy physics predictions. We construct a new parton branching algorithm which for the first time incorporates the off-shell, transverse-momentum dependent (TMD) splitting functions, defined from the high-energy limit of partonic decay amplitudes. Based on these TMD splitting functions we construct a new TMD Sudakov form factor. We present the first MC implementation of the algorithm for the evolution of the TMD and integrated parton distribution functions (PDFs). We use thi…
We introduce a general framework to construct multi-emission kernels for parton branching algorithms at the amplitude level and across different soft and collinear limits. We highlight the connection of kinematic parameterizations and recoil schemes to the underlying power counting, and discuss in detail how soft radiation can be partitioned in between different collinear configurations beyond the single-emission picture underpinning the traditional dipole and angular ordering approaches. Our work is a vital cornerstone to build parton branching algorithms which include multiply-unresolved emi…
We discuss the parton branching (PB) evolution equation for transverse momentum dependent (TMD) parton distribution functions (PDFs), especially we concentrate on the angular ordering constrain and its effect on the TMD distributions. We discuss application of the PB TMDs to precise prediction of Drell-Yan transverse momentum spectrum at LHC, stressing the role of angular ordering in the low transverse momentum region. We compare the PB implementation of the angular ordering condition with the Kimber-Martin-Ryskin-Watt (KMRW), both at the analytical and numerical level.
Partons and jets in a strongly-coupled plasma from AdS/CFT
我们给出了一个教学审查的最新进展，了解强耦合等离子体在有限温度下的硬探针的响应。等离子体是N=4超对称杨-米尔斯理论的等离子体，硬探针是虚光子，或者更准确地说，是R电流。通过规范/引力对偶，将电流与等离子体相互作用的问题映射到麦克斯韦场与嵌入AdS_5 × S^5几何中的黑洞之间的引力相互作用上。AdS/CFT结果的物理解释可以在紫外/红外对应的帮助下重建。因此，我们推断，对于足够高的能量，光子（或任何其他硬探针：夸克、胶子或介子）通过一种普遍的机制消失在等离子体中，这种机制是准民主部分子分支：电流发展出一个部分子级联，使得在分支过程的任何一步，能量几乎均等地分配给子部分子。分支率由等离子体控制，等离子体以恒定的力~ T^2作用于有色部分子。当在等离子体无限动量框架中重新解释时，相同的AdS/CFT结果表明等离子体结构函数的部分子图像，其中所有部分子都落在非常小的Bjorken x值处。对于真空中的类时电流，准民主分支意味着在强耦合的电子正电子湮没中不应该有喷流，而只有强子物质的空间各向同性分布。
We present the first determination of transverse momentum dependent (TMD) photon densities with the Parton Branching method. The photon distribution is generated perturbatively without intrinsic photon component. The input parameters for quarks and gluons are determined from fits to precision measurements of deep inelastic scattering cross sections at HERA. The TMD densities are used to predict the mass and transverse momentum spectra of very high mass lepton pairs from both Drell-Yan production and Photon-Initiated lepton processes at the LHC.
We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1 percent over a range…
The parton branching formulation of TMD evolution has recently been used to make predictions for jet observables at the Large Hadron Collider (LHC), including perturbative matching at next-to-leading order (NLO). This contribution presents results for the azimuthal Δ-ϕcorrelations in events with di-jets at large transverse momentum. It focuses on the back-to-back region of large Δ-ϕand discusses prospects for detailed studies of QCD dynamics in this region at the LHC.
NNLL Transverse Momentum Dependent evolution in the Parton Branching method
针对对撞机精密测量对强子三维结构研究的需求，本文研究TMD部分子分支方法，证明其苏达科夫形状因子与CSS方法等价，实现低qt重求和精度达NNLL阶，并提取了CS核。
We studied the evolution of jets within a medium that contains both, transverse kicks as well as medium induced coherent radiation. In this framework parton branching occurs simultaneously to scatterings within the medium, leading to the interference effects that reproduce the well known BDMPS-Z emission rates and sizeable transverse momentum broadening. We examined the relative importances of transverse momentum broadening from the coherent splittings and different types of in-medium scatterings and found a clear hierarchy of the influences from different scattering effects and deflections du…
As part of the DESY summer student program 2021, transverse momentum dependent (TMD) parton distributions obtained from the Parton Branching (PB) method were combined with next-to-leading-order (NLO) using the POWHEG method. Computations of the resulting Drell-Yan (DY) transverse momentum spectrum were performed. A good agreement of the theoretical predictions with the measurement performed by the CMS experiment at the center-of-mass energy of 13 TeV is found, at low and intermediate DY $p_{\rm T}$. The new scale choice option for the matching has been included in the CASCADE event generator.
QCD predictions for final states with multiple jets in hadron collisions make use of multi-jet merging methods, which allow one to combine consistently the contributions from hard scattering matrix elements with different parton multiplicities and parton showers. In this article I consider a multi-jet merging method that has recently been proposed to take into account the effects of transverse momentum dependent (TMD) evolution and parton shower, and present studies focusing on the application of this method to jets associated with Drell-Yan (DY) production in the region of high masses.
Jet evolution in the N=4 SYM plasma at strong coupling
在AdS/CFT对应的框架内，我们研究了通过有限温度，强耦合，N=4 SYM等离子体传播的高能R-电流的时间演化，并为我们的结果提出了一个物理图像。在这幅图中，电流分裂成一对无质量的部分子，然后通过连续的分支演化，以这样一种方式，能量被准民主地分配给分支的产物。我们指出的部分子系统的横向尺寸之间的对偶性，通过分支和径向的距离由双麦克斯韦波在AdS几何。对于类时电流，分支已经发生在真空中，在那里它产生了一个各向同性分布在横平面上的低动量部分子系统。但是在有限温度下，分支机制被介质修改，因为部分子分裂的速率通过从部分子到等离子体的横向动量的转移而增强。这种控制部分子能量损失的机制对等离子体中的能量密度敏感，但对热状态的细节不敏感。我们计算寿命的电流为各种运动学制度，并提供物理解释的其他相关的量，所以像介子屏蔽长度，拖曳力，或尾随字符串，这是以前计算通过AdS/CFT技术。
Collinear and transverse momentum dependent (TMD) parton densities are obtained from fits to precision measurements of deep inelastic scattering (DIS) cross sections at HERA. The parton densities are evolved by DGLAP evolution with next-to-leading-order (NLO) splitting functions using the parton branching method, allowing one to determine simultaneously collinear and TMD densities for all flavors over a wide range in $x$, $μ^2$ and $k_t$, relevant for predictions at the LHC. The DIS cross section is computed from the parton densities using perturbative NLO coefficient functions. Parton densiti…
Giovannini's parton branching equation is integrated numerically using the 4th-order Runge-Kutta method. Using a simple hadronisation model, a charged-hadron multiplicity distribution is obtained. This model is then fitted to various experimental data up to the TeV scale to study how the Giovannini parameters vary with collision energy and type. The model is able to describe hadronic collisions up to the TeV scale and reveals the emergence of gluonic activity as the centre-of-mass energy increases. A prediction is made for $\sqrt{s}$ = 14 TeV.
One of the main theoretical systematics in studies of final states with large jet multiplicities at high-energy hadron colliders is associated with the merging of QCD parton showers and hard-scattering matrix elements. We present a method to incorporate the physics of transverse momentum recoils due to initial-state shower evolution into multi-jet merging algorithms by using the concept of transverse momentum dependent (TMD) distributions and the associated parton branching. We investigate the dependence on the merging scale and illustrate the impact of the new method at the level of both excl…
The Parton Branching evolution package uPDFevolv2
介绍用于 DGLAP 演化共线和 TMD 部分子密度的软件包 uPDFevolv2，提供理论、实现及使用指南，作为版本 2.5.03 的技术发布说明。
Transformation of transverse momentum distributions from Parton Branching to Collins-Soper-Sterman framework
本文首次建立了从部分子分支（PB）框架到Collins-Soper-Sterman（CSS）形式的TMD部分子分布变换方法，利用Drell-Yan模拟谱确定的Collins-Soper核实现变换，并将演化后的PB-TMD与ART23分布进行了比较验证。
Radiative parton energy loss in expanding quark-gluon plasma with magnetic monopoles
本文研究了具有磁单极子的膨胀夸克-胶子等离子体中的辐射部分子能量损失。我们发现，对于在晶格模拟中获得的热单极子的真实数密度，部分子在单极子上的再散射可以大大增加RHIC和LHC能量下$AA$碰撞产生的等离子体的能量损失。然而，与先前的预期相反，磁单极子并不导致能量损失的表面优势。
Soft-gluon coupling and the TMD parton branching Sudakov form factor
本文在部分子分支框架中引入软胶子物理耦合，实现TMD分布的NNLL精度，并给出Collins-Soper核，为LHC及未来对撞机上的物理预测奠定基础。
Transverse Momentum Dependent (TMD) parton distributions obtained from the Parton Branching (PB) method are combined with next-to-leading-order (NLO) calculations of Drell-Yan (DY) production. We apply the MCatNLO method for the hard process calculation and matching with the PB TMDs. We compute predictions for the transverse momentum, rapidity and $ϕ^*$ spectra of Z-bosons. We find that the theoretical uncertainties of the predictions are dominated by the renormalization and factorization scale dependence, while the impact of TMD uncertainties is moderate. The theoretical predictions agree wel…
Photon emission from out of equilibrium dissipative parton plasma
利用二阶Israel-Stewart流体力学方法讨论了相对论重离子碰撞中部分子等离子体中粘性对光子产生的影响。我们发现，由于在化学非平衡等离子体中的粘性效应，光子产生率可以提高几个因素。
On the role of soft gluons in collinear parton densities and parton shower event generators
本文利用Parton Branching方法求解DGLAP方程，发现软胶子在共线部分子密度演化中对于发散项抵消至关重要，其非微扰Sudakov形式因子影响包容性分布，但对末态强子谱和喷注几乎无作用。
Towards a consistent description of in-medium parton branching
超相对论性重离子碰撞是研究极端温度和密度条件下的QCD物质的一个机会窗口，例如夸克-胶子等离子体。在几种可能性中，对喷射淬火的研究--部分子分支的介质能量损失修改的通用名称--是评估这种新物质状态的性质的有力工具。部分子簇射的描述在真空（受控参考）中得到了很好的理解，并且可以通过喷流测量在实验上获得该过程的介质诱导修改。然而，目前的实验数据，不能完全描述只有能量损失现象。横向动量展宽和退相干效应，无论是理论上建立了现在，它们之间的相互作用是必不可少的，以建立一个一致的图片的介质修改的部分子分支，并实现正确的描述目前的实验数据。在本文中，我们将介绍解决这种统一描述的最新进展。
Comparison of CMS measurements with predictions at NLO applying the Parton Branching Method and PYTHIA
本文介绍了DESY暑期学校项目中将未纳入RIVET的CMS分析实现并验证的工作，并将测量结果与标准部分子簇射蒙特卡洛生成器及Parton-Branching TMDs的预测进行了比较。
The theoretical description of Drell-Yan (DY) transverse momentum spectra over wide kinematic regions in energy, mass and transverse momentum requires not only fixed-order perturbative QCD calculations but also soft-gluon QCD resummations to all orders of perturbation theory. The latter are traditionally accomplished either by Parton Showers (PS) with Monte Carlo event generators or by (different versions of) analytical procedures. In this work we focus on issues involved in the matching of the fixed-order calculation and resummation, especially in the moderate to low mass and $p_{\bot}$ regio…
What can we learn from the Parton Branching method in QCD?
本文回顾了Parton Branching方法在TMD部分子分布及Monte Carlo生成器中的最新进展，分析了纳入光子与重电弱玻色子辐射等关键改进，并通过与Collins-Soper-Sterman框架的比较突出了PB Sudakov形式因子精度的提升及非微扰效应建模的意义。
Origin of Temperature of Quark-Gluon Plasma in Heavy Ion Collisions
最初在RHIC和LHC中产生的夸克胶子物质没有温度。夸克-胶子等离子体具有高温。从这种夸克-胶子物质到夸克-胶子等离子体是早期热化或温度的快速创造。弹性三部分子散射在这个过程中起着关键作用。温度来源于夸克-胶子物质中的二部分子散射、三部分子散射、四部分子散射等。
Glueball-Induced Partonic Energy Loss in Quark-Gluon Plasma
讨论了在解除禁闭温度$T_c$以上的夸克-胶子等离子体中，部分子喷注与标量和赝标胶球相互作用时的能量损失。结果表明，这种机制的损失是相当重要的，并可能发挥重要的作用所观察到的射流淬火。
Strangeness Production in Chemically Non-Equilibrated Parton Plasma
研究了在RHIC和LHC能区产生的胶子主导的部分子等离子体平衡过程中的奇异性产生。在一维膨胀系统中，部分子密度随时间的演化由一组速率方程来描述。奇异值的产生取决于初始的化学平衡水平，在我们的例子中，部分子密度将远离完全平衡。我们研究了胶子碎裂对末态奇异度的影响。
Sonic Mach Cones Induced by Fast Partons in a Perturbative Quark-Gluon Plasma
通过把快部分子看作扰动介质的外部色场的源，导出了快部分子穿过弱耦合夸克-胶子等离子体时所沉积的能量和动量的时空分布.然后，我们使用我们的结果作为源项的线性流体动力学方程的介质。结果表明，当部分子以超音速运动时，该解包含一个音速马赫锥和一个耗散尾迹。
The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy scales, transverse degrees of freedom cannot be neglected, and finite-order perturbative calculations have to be combined with resummed calculations to all orders in the QCD running coupling in order to obtain reliable theoretical predictions, capable of describing experimental measurements. This is traditionally done either by analytic resummation methods or by…
Equilibration and Particle Production in an Increasingly Strongly Interacting Parton Plasma
本文报道了相对论性重离子碰撞中的一种新的平衡态，即相互作用越来越强的部分子等离子体的平衡态，以及这种平衡态对平衡态、开粲、光子和双轻子产生的影响。部分子等离子体是一种特殊的多体系统，它包含着关于平衡态的新物理。这可能是部分子等离子体所独有的。
The description of the in-medium modifications of partonic showers has been at the forefront of current theoretical and experimental efforts in heavy-ion collisions. It provides a unique laboratory to extend our knowledge frontier of the theory of the strong interactions, and to assess the properties of the hot and dense medium (QGP) that is produced in ultra-relativistic heavy-ion collisions at RHIC and the LHC. The theory of jet quenching, a commonly used alias for the modifications of the parton branching resulting from the interactions with the QGP, has been significantly developed over th…
NLO Analysis of Small-$k_T$ Region in Drell-Yan Production with Parton Branching
本文利用部分子分支方法导出的 TMD 部分子密度和 MC@NLO 风格 NLO 计算，通过拟合 Drell-Yan 横动量谱确定内禀 $k_T$ 分布宽度，发现该宽度与 Drell-Yan 质量和质心能量无关。
We consider the associated production of electroweak gauge bosons and charm or beauty quark jets at the LHC using the $k_T$-factorization framework. We apply the transverse momentum dependent (TMD) parton distributions in a proton obtained from the Parton Branching (PB) method as well as from the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. For the PB approach, our prescription merges the standard leading order ${\cal O}(αα_s)$ $k_T$-factorization calculations with several tree-level next-to-leading order ${\cal O}(αα_s^2)$ off-shell production amplitudes. For the CCFM scenar…
Quenching of Hadron Spectra due to the Collisional Energy Loss of Partons in the Quark-Gluon Plasma
我们估计了在超相对论重离子碰撞中由于硬部分子碰撞初始阶段能量损失而引起的能量损失分布，并研究了强子谱的猝灭。
Open Charm Production in an Equilibrating Parton Plasma
本文计算了胶子占主导地位的部分子等离子体平衡过程中的开粲产生，给出了一组速率方程，给出了温度和部分子密度随时间的变化。包括预热产生在内，开粲产生相对于初始胶子熔合的总增强敏感地依赖于初始部分子密度和有效温度。讨论了初始部分子相空间分布中的空间动量关联对前热粲产生的影响。
Fast partons as a source of energy and momentum in a perturbative quark-gluon plasma
通过把快部分子看作与介质相互作用的外部色场的源，导出了快部分子穿越微扰夸克-胶子等离子体时所沉积的能量和动量的时空分布.我包括介质的响应屏蔽的快部分子的色场通过纳入介电函数和比较，未屏蔽的结果。
Radiative Energy Loss of High Energy Partons Traversing an Expanding QCD Plasma
根据Bjorken模型，我们解析地研究了高能部分子通过纵向膨胀的有限尺寸QCD等离子体时的介质诱导能量损失。我们扩展的BDMPS形式主义已经应用到静态介质的情况下，夸克击中连续层的物质的温度降低，我们表明，由此产生的辐射能量损失可以大到6倍，相应的一个在静态等离子体在参考温度$T = T (L)$，这是达到后，夸克传播距离$L$。
We present an algorithm that evolves hard processes at the amplitude level by dressing them iteratively with (massless) quarks and gluons. The algorithm interleaves collinear emissions with soft emissions and includes Coulomb/Glauber exchanges. It includes all orders in $N_{\mathrm{c}}$, is spin dependent and is able to accommodate kinematic recoils. Although it is specified at leading logarithmic accuracy, the framework should be sufficient to go beyond. Coulomb exchanges make the factorisation of collinear and soft emissions highly non-trivial. In the absence of Coulomb exchanges, we show ho…
Parton energy loss in an expanding quark-gluon plasma: Radiative vs collisional
我们比较了膨胀夸克-胶子等离子体中辐射和碰撞部分子的能量损失。采用光锥路径积分法计算了辐射能量损失。碰撞能量损失的计算使用Bjorken方法与准确的治疗的二进制碰撞运动学。我们的数值结果表明，RHIC和LHC条件下的碰撞能量损失是相对较小的辐射相比。我们发现，在高能量的轻夸克相比，重夸克的辐射能量损失的增强。
The b-u skewed parton distributions
讨论了b-u偏态部分子分布. SPD允许重叠和共振贡献的明确叠加，并且它们的零阶矩表示B π转变形状因子。最大反冲时的形状因子值为F+（0）= F_0（0）=0.22，误差为0.05，与B -π π分支比的测量结果一致。计算了半轻子B π衰变的分支比。
Screening of a Moving Parton in the Quark-Gluon Plasma
用半经典输运理论计算了部分子在夸克-胶子等离子体中运动的屏蔽势。发现了在部分子速度方向上具有极小值的各向异性势，并由此讨论了可能的新束缚态和J/psi离解。
The description of the Drell-Yan (DY) transverse momentum spectrum requires matching of fixed order QCD calculations with soft gluon resummation up to all orders in the QCD coupling. It has been noticed in the literature that a consistent description of DY data in a wide kinematic regime from fixed-target to LHC energies is problematic. In this talk the predictions for transverse momentum spectrum of DY data coming from experiments in very different kinematic ranges (NuSea, R209, Phenix, LHC 8 TeV and 13 TeV center-of-mass energies $\sqrt{s}$) are calculated by applying transverse momentum dep…
Condensation of a Strongly Interacting Parton Plasma into a Hadron Gas in High Energy Nuclear Collisions
本文研究了RHIC能区部分子等离子体向强子气体跃迁过程中色屏蔽效应的影响。结果发现，正如预期的那样，色屏蔽本身作为一个显着的障碍强子化。因此，与真空中发生的情况相比，部分子-强子转换将被延迟和延长。由于持续的膨胀，产生的强子密度降低。部分子平衡也被证明是严重破坏的过程中。
Small-x single-particle distributions in jets from the coherent branching formalism
我们计算内夸克和胶子喷流的相干分支形式主义，它恢复领导和下一个领导的对数贡献的单部分子分布。这种形式主义是在修改的领先对数近似（MLLA）的基础上，它保存的能量。对于演化变量Y=ln[Eθ/Q_0]的一个宽的前渐近范围，我们发现在MLLA和相干分支形式中计算的单个部分子分布的形状和范数有明显的不同。对于渐近大值Y>5-10，范数的差异持续存在，而形状的差异消失。通过这种方式，我们的数值研究描绘了两种方法的可靠应用所需的射流能量尺度。我们还研究了单部分子分布对强子化标度Q_0和Λ_QCD的依赖性，并在相干分支形式下计算了夸克喷注和胶子喷注中的夸克和胶子分布。
Langevin dynamics of $J/ψ$ in a parton plasma
本文研究了在夸克-胶子等离子体的极早期产生的$c \bar c$对的布朗运动。对一维朗之万方程进行了形式求解，得到了小时间和大时间下的纯力学性质。随机平均方差进行检查，以提取与膨胀和电离的束缚态的时间尺度。简单的数值估计的时间尺度进行比较与其他机制的$J/ψ$抑制。
The incorporation of running $α_s$ for the gluon emission vertex in calculations of radiative parton energy loss in a quark-gluon plasma is discussed. It is argued that the virtuality scale for running $α_s$ for induced gluon emission is determined by the square of the transverse momentum of the emitted gluon rather than by the square of the invariant mass of the final two-parton state often used in the literature.
The small kt-region in Drell-Yan production at next-to-leading order with the Parton Branching Method
本研究在次领头阶下，利用 Parton Branching 方法研究 Drell-Yan 产生中的小 kT 区域，提取非微扰内禀横动量分布，并分析其对 DY 质量和能量的依赖性。
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