The non-vanishing of gluonic pole matrix elements can explain the appearance of single spin asymmetries in high-energy scattering processes. We use a spectator framework approach to investigate the spectral properties of quark-quark-gluon correlators and use this to study gluonic pole matrix elements. Such matrix elements appear in principle both for distribution functions such as the Sivers function and fragmentation functions such as the Collins function. We find that for a large class of spectator models, the contribution of the gluonic pole matrix element in fragmentation functions vanishes. This outcome is important in the study of universality for fragmentation functions and confirms findings using a different approach.
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized compo…
We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation f…
Gluonic nucleon energy correlators and fracture functions for Color Glass Condensate
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Shandong University（山东大学）；École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Chulalongkorn University（朱拉隆功大学）
The fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson are derived up to QCD next-to-leading order (NLO). They are further computed numerically and presented in figures precisely. In order to reach a higher accuracy, we have also tried properly to apply them to estimating the $B_c$ and $B_c^*$ production at a $Z$-factory (an $e^+e^-$ collider running at the energy of the $Z$-boson pole).
In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium $J/Ψ$ or $Υ$. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. $μ_{F}=3 m_c$ for $c\to J/Ψ$ and $μ_{F}=3m_b$ for $b\to Υ$, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial applicati…
Charm-quark fragmentation with an effective coupling constant
我们使用最近提出的一个非微扰模型，基于一个有效的强耦合常数和自由的可调参数，研究e+e-湮灭中的c味强子产生。在微扰碎裂函数的框架下描述了粲夸克的产生，包括NLO系数函数、NLL非单重态的DGPs演化和NNLL大尺度的再确认。我们通过在NNLO近似下的有效耦合常数来模拟强子化效应，并将我们的结果与在Z 0极点和Upperdance（4S）共振下的实验数据进行了比较。我们发现，在实验和理论的不确定性范围内，当x<1-Lambda/m_c时，我们的模型能够给出ALEPH D ~*~+介子谱的合理描述。当与BELLE和CLEO在x空间中的D和D^* 数据进行比较时，出现了更严重的差异。在误差范围内，我们的模型仍然能够再现所有考虑的数据集的前十个梅林时刻。然而，相当大的理论不确定性要求一个完整的NNLO/NNLL分析。
Extraction of the x-dependence of the non-perturbative QCD b-quark fragmentation distribution component
利用最近在Z极记录的$e^+e^- \to b \bar{b}$事件中获得的b夸克碎裂分布的测量结果，独立于任何强子物理模型，提取了该分布的非微扰QCD分量。这种分布只取决于微扰QCD分量的定义方式。当微扰QCD分量取自部分子簇射Monte-Carlo时，非微扰QCD分量与Lund或Bowler模型的结果相当相似。当微扰QCD分量是解析NLL计算的结果时，非微扰QCD分量必须在非物理区域中扩展，因此不能用任何强子模型来描述。在目前研究的用于表征这两种情况的两个例子中，提取的非微扰QCD分布具有相同的形状，在第二种方法中被简单地转换为更高的x值，说明了解析微扰QCD方法比部分子簇射发生器更能解释更软的胶子辐射。
We study asymptotically free SU($N_c$) gauge theories with ${\cal N}=1$ supersymmetry, including the purely gluonic theory and theories with $N_f$ copies of a pair of massless chiral superfields in the respective representations $R$ and $\bar R$ of SU($N_c$). The cases in which $R$ is the fundamental representation and the symmetric and antisymmetric rank-2 tensor representation are considered. We calculate Padé approximants to the beta functions for these theories in the $\overline{\rm DR}$ scheme up to four-loop order for the gluonic theory and up to three-loop order for the theories with ma…
In covariant gauges, the gluonic mass gap in Yang-Mills theory manifests itself in the basic observation that the massless pole in the perturbative gluon propagator disappears in nonperturbative calculations, but the origin of this behavior is not yet fully understood. We summarize a recent study of the respective dynamics with Dyson-Schwinger equations in Landau-gauge Yang-Mills theory. We identify the parameter that distinguishes the massive Yang-Mills regime from the massless decoupling solutions, whose endpoint is the scaling solution. Similar to the PT-BFM scheme, we find evidence that ma…
We determine the gluonic spectral function $SU(3)$ Yang-Mills theory as well as we found fermionic spectral functions in the strong quenched QED where we found new solutions. Our novel technique provides solutions with the usual branch cut for propagators while not showing any pole structure at the first Riemann sheet (identical with entire complex plane) of complex square of momentum. Implications and further utilizations are briefly adressed for QCD and Standard model calculations.
The forward-backward asymmetry of $b$-quarks measured at LEP in $e^+e^-$ collisions at the Z pole, $A_{FB}^{0,b}|^{\rm exp} = 0.0992\pm0.0016$, remains today the electroweak precision observable with the largest disagreement (2.8$σ$) with the Standard Model theoretical prediction, $A_{FB}^{0,b}|^{\rm th} = 0.1037\pm0.0008$. The dominant systematic uncertainties are due to QCD effects --- $b,c$-quark showering and fragmentation, and $B,D$ meson decay models --- which have not been revisited in the last 20 years. We reassess the QCD uncertainties of the eight original LEP measurements of $A_{FB}…
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, $η= m_c^2/m_b^2 \sim 1/10$, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two--mass case is…
