Some news about generalised parton distributions
Markus Diehl
我简要地讨论了一些最近的发展（并回顾一些旧的消息）在理论和现象学的广义部分子分布。
I briefly discuss some recent developments (and recall some old news) in the theory and phenomenology of generalised parton distributions.
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Unintegrated generalised parton distributions
我们展示了如何从已知的常规部分子分布q（x，mu^2）和g（x，mu^2）中计算出在部分子横动量上未积分的质子的广义（或偏斜）部分子分布H（x，xi; k_t^2，mu^2），对于小的偏斜参数xi。我们证明了数值计算的过程中的倾斜未积分胶子。我们还提供了一个简单的近似唯象形式的分布，这可能是用来更快速的预测观测。
The operator definition of generalised transverse-momentum-dependent (GTMD) distributions is exploited to compute for the first time the full set of one-loop corrections to the off-forward matching functions. These functions allow one to obtain GTMDs in the perturbative regime in terms of generalised parton distributions (GPDs). In the unpolarised case, non-perturbative corrections can be incorporated using recent determinations of transverse-momentum-dependent (TMD) distributions. Evolution effects for GTMDs closely follow those for TMDs and can thus be easily accounted for up to next-to-next…
Pion generalised parton distributions are calculated within the framework of the Nambu--Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three dimensional momentum cutoff scheme, the four dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalised parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluat…
Generalised Parton Distributions of the Pion on the Transverse Lattice
本文用横格点规范理论中的光锥波函数计算了大N_c下π介子的夸克广义部分子分布。发现π介子的有效尺寸随动量转移的增加而减小。给出了与有限束缚态光锥能量条件相一致的波函数对光锥动量依赖性的解析解。这导致了对端点附近分布行为的简单，通用的预测，补充了数值DLCQ数据。
We discuss the use of machine learning techniques in effectively nonparametric modelling of generalised parton distributions (GPDs) in view of their future extraction from experimental data. Current parameterisations of GPDs suffer from model dependency that lessens their impact on phenomenology and brings unknown systematics to the estimation of quantities like Mellin moments. The new strategy presented in this study allows to describe GPDs in a way fulfilling theory-driven constraints, keeping model dependency to a minimum. Getting a better grip on the control of systematic effects, our work…
A Simple Model for Generalised Parton Distributions of the Pion
在这里，我们提出了一个扩展我们的模型的π介子，我们以前用来计算其对角结构函数，关闭向前的情况下。在手征极限（m_pi=0）下计算了非正向γ ^* pi -> γ ^* pi散射振幅的虚部，并与扭曲2和扭曲3的广义部分子分布H，H3，H3波浪线有关。非微扰效应，与π介子的大小和仍然保持规范不变性，包括在内。得到并讨论了H、H_3和H_3代子之间的新关系。
Generalised parton distributions at small x
我们证明实际使用的Shuvaev积分变换方法来计算的偏斜分布，需要描述衍射过程，直接从传统的对角全球部分子分布。我们解决了对这一程序提出的疑问。我们强调，这种方法，一方面，满足所有的理论要求，另一方面，是一致的DVCS数据在NLO。我们构建了一个易于访问的软件包来计算这些偏态分布。
These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon International School of Physics in 2021.
A toy model for generalised parton distributions
我们给出了一个简单模型的结果的对角和非对角价夸克分布的π。我们表明，结构可以实现规范不变的方式。该模型对动量和规则的有效性提出了质疑，并给出了Wandzura-Wilczek模型对twist-3 GPD的反例。
Generalised parton distributions at HERA and prospects for COMPASS
我们提出了一个模型的广义部分子分布的基础上的前向anqueries在DGSTZ区域。我们讨论了参数化的某些方面，作为依赖于t，因式分解和非因式分解的方法，其中t是在强子顶点交换的四个动量的平方。然后，将该模型的预测与来自H1和ZEUS的DVCS截面以及相关的可观察到的偏斜因子进行比较，偏斜因子定义为以下比值虚振幅：$R \equiv {Im {\cal A} (γ^*+p \to γ+p)\lfrestriction{t=0}} / {Im {\cal A} (γ^*+p \to γ^* +p)\lfrestriction{t=0}}$。它是一个有趣的量，包括非正向运动学和非对角效应。最后，我们讨论了束流电荷不对称性，这肯定是最敏感的观察到的不同的假设中所需的GPD参数化。我们表明，近似的t依赖导致显着差异的预测在HERMES运动域和前景给出了指南针。
Generalised Parton Distributions: A Dyson-Schwinger approach for the pion
我们用耦合的Bethe-Salpeter和Dyson-Schwinger方法计算了夸克的广义部分子分布H和夸克双分布。我们使用解析表达式的启发，戴森-Schwinger和Bethe-Salpeter方程的数值分辨率。我们得到了一个解析表达式的π介子广义部分子分布在一个低尺度。我们的模型满足大多数所需的对称性和比较非常好的实验π形状因子或价部分子分布函数的实验数据。此外，我们强调了所谓的脉冲近似的局限性，它打破了对称性时，计算价部分子分布函数。这样做，我们引入了以前被忽视的新术语。最后，我们还阐明了π介子GPD的一个特殊性质：Polyakov软π介子定理。
Yangian and SUSY symmetry of High Spin Parton Splitting Amplitudes in Generalised Yang-Mills Theory
在假定张量胶子散射振幅具有杨氏对称性的条件下，计算了高自旋部分子分裂振幅。由此产生的分裂振幅与早期的计算，这是基于BCFW递归关系。由此产生的公式统一了所有已知的分裂概率发现较早的规范场理论。它描述了整数和半整数自旋粒子的分裂概率。我们还检查了分裂概率满足广义Kounnas-Ross N=1超对称关系，这暗示了基础理论可以以明确的超对称方式制定的事实。
Searching for New Physics Inside Jets with the Herwig 7 Generalised Parton Shower
本文研究了包含标准模型和超出标准模型辐射的部分子喷注演化，聚焦于质量较大的Z'玻色子现象学。通过Herwig 7框架模拟Z'在对数增强区域的产生，探讨了SM与BSM喷注的相互作用，识别了区分Z'喷注与常规信号的动量学特征。
From Bethe-Salpeter Wave Functions to Generalised Parton Distributions
我们回顾了最近的作品中的戴森-施温格形式主义的广义部分子分布的建模。我们强调如何协变计算，使用脉冲近似，允许一个满足大多数的GPD的理论约束。特别注意手征性质，特别是所谓的软π介子定理，以及它与轴矢量沃德-高桥恒等式的联系。同时也说明了脉冲近似的局限性。超越脉冲近似计算进行审查，在前进的情况下。最后，我们强调光锥波函数的重叠的优点，并可能的方式来构建协变GPD模型在这个框架内，在两体近似。
We report on the use of Feynman-Hellmann techniques to calculate the off-forward Compton amplitude (OFCA) in lattice QCD. At leading-twist, the Euclidean OFCA is parameterised by the Mellin moments of generalised parton distributions (GPDs). Hence we extract GPD moments for two values of the soft momentum transfer, $t=-1.10, -2.20\;\text{GeV}^2$ and zero-skewness kinematics at an unphysical pion mass of $m_π\approx 470\;\text{MeV}$. This includes the first determination of the $n=4$ moments.
We revisit the evolution of generalised parton distributions (GPDs) in momentum space. We formulate the evolution kernels at one-loop in perturbative QCD (pQCD) in a form suitable for numerical implementation and that allows for an accurate study of their properties. This leads to the first open-source implementation of GPD evolution equations able to cover the entire kinematic region and allowing for heavy-quark-threshold crossings. The numerical implementation of the GPD evolution equations is publicly accessible through the APFEL++ evolution library and is available within the PARTONS frame…
Pion and kaon structural properties provide insights into the emergence of mass within the Standard Model and attendant modulations by the Higgs boson. Novel expressions of these effects, in impact parameter space and in mass and pressure profiles, are exposed via $π$ and $K$ generalised parton distributions, built using the overlap representation from light-front wave functions constrained by one-dimensional valence distribution functions that describe available data. Notably, e.g. $K$ pressure profiles are spatially more compact than $π$ profiles and both achieve near-core pressures of simil…
One-loop matching for leading-twist generalised transverse-momentum-dependent distributions
本文提出了将领头扭度广义横动量依赖分布（GTMDs）匹配到广义部分子分布（GPDs）的单圈匹配系数，通过计算部分子双局域关联子的辐射修正提取匹配函数，揭示了 GTMDs 在匹配和演化下的复杂动力学混合行为。
Introduction to GPDs and TMDs
广义部分子分布（GPD）和横向动量相关部分子分布（TMD）描述了强子三维结构的互补方面。我们讨论它们之间的关系，并回顾重要的理论结果，关于它们的性质和它们与物理观测量的联系。
Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a next-to-leading order analysis and a careful study of evolution effects, we exhibit non-trivial generalised parton distributions with arbitrarily small imprints on deeply virtual Compton scattering observables. This means that in practice the reconstruction of generalised parton distributions from measurements, known as the deconvolution problem, does not pos…
Clear windows onto emergent hadron mass (EHM) and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure, many of which are accessible via generalised parton distributions (GPDs). Beginning with algebraic GPD Ansaetze, constrained entirely by hadron-scale $π$ and $K$ valence-parton distribution functions (DFs), in whose forms both EHM and Higgs boson influences are manifest, numerous illustrations are provided. They include the properties of electromagnetic form factors, impact parameter space GPDs, gravitational form factors and associat…
Combining lattice QCD and phenomenological inputs on generalised parton distributions at moderate skewness
本文在贝叶斯框架中引入模拟 lattice QCD 数据，结合满足理论约束的机器学习 GPD 模型，系统评估数据精度、相关性与运动学覆盖对中等 ξ 下 GPD 提取的影响。
Extraction of the Compton Form Factor H from DVCS measurements at Jefferson Lab
在广义部分子分布的框架下，我们研究了在Jefferson实验室A厅测量的与螺旋度相关和独立的截面以及在B厅测量的束流自旋不对称性。我们对这些数据进行全局拟合，并拟合每个运动学箱。我们提取的实部和虚部的康普顿形状因子$\mathcal{H}$的主要假设下的优势的广义Parton分布$H$和扭转2的准确性。我们讨论了我们的结果，并比较以前的提取以及VGG模型。我们特别注意对$\mathcal{H}$提取的误差估计。
One-loop evolution of twist-2 generalized parton distributions
重新推导所有twist-2夸克和胶子算子的GPDs在强耦合常数领头阶的单圈演化核，验证其基本性质，并在APFEL++和PARTONS框架中给出数值结果。
Reconstructing generalised parton distributions from the lattice off-forward Compton amplitude
本研究利用格点QCD的费曼-海尔曼方法测定离轴康普顿振幅结构函数，在非物理π介子质量和多组软动量转移条件下测试两种GPD重构方法，结果与唯象及其他格点研究吻合，并明确了需控制的系统误差。
Sketching the pion's valence-quark generalised parton distribution
为了有效地学习广义部分子分布（GPD）的测量，它是可取的计算它们使用的框架，可以潜在地连接经验信息与标准模型的基本特征。我们基于QCD的Dyson-Schwinger方程的彩虹梯截断，并以π介子的价缀饰夸克GPD，$H_π^{\rm v}(x,ξ,t)$为例，给出了一种计算方法。我们的分析主要集中在$ξ=0$，虽然我们也利用了RL截断的保序性质，将$H_π^{\rm v}(x,ξ=\pm 1,t)$与π介子的价夸克部分子分布振幅联系起来。我们解释了迄今为止用来定义π介子的价缀饰夸克GPD的脉冲近似一般是无效的，因为忽略了胶子的贡献，胶子将缀饰夸克束缚到π介子中。一个简单的校正，使我们能够确定一个切实可行的改进近似$H_π^{\rm v}(x,0,t)$，表示为一个单一的幅度的拉东变换。因此，我们得到的结果$H_π^{\rm v}(x,0,t)$和相关的影响参数依赖的分布，$q_π^{\rm v}(x,|\vec{b}_\perp|)$，这提供了一个定性的声音图片的介子的打扮夸克结构在强子尺度。我们发展的分布规模$ζ=2\,$ GeV，以便在未来的比较与实验或其他非微扰方法的结果。
Presentations from DIS2002 in Krakow
我在DIS 2002上的两个演讲，关于广义部分子分布和核阴影。在附录中，我总结了会谈后的一些讨论。
Spin and 3D structure: theoretical advances
该研究针对强子结构的理论进展，综述了自旋依赖部分子分布等多方面的新结果与发展，聚焦相关分布及幂次修正计算。
Exclusive vector-quarkonium photoproduction at NLO in alpha_s in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation
本文在共线因子化下完成矢量夸克偶素遍举光生的完整单圈计算，引入GPD演化并用DLA HEF重求和高能对数修正，使结果符合HERA数据并降低标度敏感性。
We introduce a new family of Generalised Parton Distribution models able to fulfil by construction all the theoretical properties imposed by QCD. These models are built on standard Parton Distribution Functions and extended to off-forward kinematics through a well-defined procedure. We apply this strategy on the pion, first handling a simple but insightful algebraic model, and then exploiting state-of-the-art computations obtained in continuum QCD. We compare these models with a more standard one relying on an xFitter extraction of the pion Parton Distribution Functions. The results for both q…
Accessing chiral-even quark generalised parton distributions in the exclusive photoproduction of a $ γπ^{\pm} $ pair with large invariant mass in both fixed-target and collider experiments
本文在大不变质量γπ±对子独家光生过程中，基于共线因子化框架计算散射振幅，并估算JLab、COMPASS、EIC和LHC上的截面与极化不对称度，为小偏斜度下研究GPDs开辟新途径。
We present in this letter the first systematic feasibility study of accessing generalised parton distributions of the pion at an electron-ion collider through deeply virtual Compton scattering at next-to-leading order. It relies on a state-of-the-art model, able to fulfil by construction all the theoretical constraints imposed on generalised parton distributions. Strikingly, our analysis shows that quarks and gluons interfere destructively and that gluon dominance could be spotted by a sign change of the DVCS beam spin asymmetry.
We extend our studies of a new class of $2 \to 3$ exclusive processes using the collinear factorisation framework by considering the exclusive photoproduction of a $γ\,ρ$ pair, in the kinematics where the pair has a large invariant mass, {and the outgoing $ ρ$-meson has a sufficiently large transverse momentum to not resonate with the nucleon}. We cover the whole kinematical range from medium energies in fixed target experiments to very large energies of colliders, by considering the experimental conditions of JLab~12-GeV, COMPASS, future EIC and LHC (in ultra-peripheral collisions) cases. One…
Universality of the EMC Effect
利用有效场论，我们研究了核子部分子分布的核修正（例如EMC效应）。我们表明，核部分子分布的形状畸变的普遍性（Bjorken x和原子序数（A）的依赖性的因式分解）是模型无关的，自然出现在有效场论。然后，我们扩展我们的分析，研究类似的核修改的同位旋和自旋依赖的部分子分布和广义部分子分布。
Physics Objectives for Future Studies of the Spin Structure of the Nucleon
物理学的前景显示在核子上的电子或正电子散射的未来实验，对量子色动力学的背景下的核子的角动量结构的深入和全面的了解。排斥反应中广义部分子分布的测量和半包容深度非弹性散射中正向部分子分布的精确测定被确定为主要的物理课题。要求进行了讨论，为下一代的高光度固定目标的实验在能量范围30-200 GeV。
We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elemen…
Hemisphere mass up to four-loops with generalised $k_t$ algorithms
本文利用通用$ k_t $算法计算了非全局半球质量可观察量的四重循环分布，并展示了忽略非全局对数对现象学预测的不可靠性。
Exclusive meets inclusive at small Bjorken-$x_B$: how to relate exclusive measurements to PDFs based on evolution equations
该研究在α_s领头阶下探究广义部分子分布（GPD）与部分子分布函数（PDF）的关联，提出量化二者关联固有系统不确定性的方法，可推广至高阶与小x重求和，对电子离子对撞机提取部分子径向分布具有重要意义。
A Continuum Schwinger Method to Study the Pion's Generalized Parton Distribution
本文提出一种连续施温格尔方法，用于研究π介子的广义部分子分布，满足QCD约束，并用于计算深度虚拟康普顿散射的康普顿形变因子。
Kaon GTMDs in the Dyson-Schwinger equations using contact interaction
本文在 Dyson-Schwinger 方程框架下用接触相互作用计算 kaon 的多 twist GTMD，并导出 GPD、TMD、Wigner 分布及自旋-轨道关联和横向自旋畸变。
Proton internal pressure from deeply virtual Compton scattering on collider kinematics
本文提出次领头阶形式体系，在深度虚康普顿散射全局拟合中引入真正的胶子自由度，以改进核子内部压强与剪切力分布的提取，并评估未来电子-离子对撞机扩展运动学范围对降低不确定性的作用。
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