Fatma P. Aslan, Matthias Burkardt, Marc Schlegel
While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. As an example, we use the nonforward generalization of $g_T(x)$, to illustrate how twist-3 GPDs can provide transverse position information about that force.
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The interaction dependent part of the $x^2$-moment of the twist-3 polarized parton distribution $g_2(x)$ is related to the transverse force acting on the active quark in deep-inelastic scattering off a transversely polarized nucleon immediately after it has absorbed the virtual photon. Similarly, the $x^2$-moment of the chirally odd twist-3 unpolarized parton distribution $e(x)$ can be related to the transverse force experienced by a transversely polarized quark ejected from a transversely polarized nucleon.
While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. We demonstrate how twist-3 GPDs can be used to provide transverse position information about that force.
Generalized Parton Distributions (GPDs) provide information on the distribution of quarks in impact paarmeter space. For transversely polarized nucleons, these impact parameter distributions are transversely distorted and this deviation from axial symmetry leads on average to a net transverse force from the spectators on the active quark in a DIS experiment. %The strength of that force can be related to twist-3 PDFs. This force when acting along the whole trajectory of the active quark leads to a transverse single-spin asymmetries. For a longitudinally polarized nucleon target, the transverse …
We study the semi-classical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semi-classical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was find, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a DIS experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between tha…
In this proceeding, we review our recent work in which we performed the first global analysis of nuclear modified Transverse Momentum Distribution Functions (TMDs). We demonstrate for the first time that the global set of TMD experimental data from HERMES, E866, E772, RHIC, ATLAS, and CMS, can be described using a simple model which accounts for the nuclear modifications for the TMDs as a non-perturbative correction. Using this model, we extract the nuclear modified TMDs for the first time.
Introduction to transverse momentum imaging
本文介绍横向动量成像的基本概念与应用，适用于高能物理研究生课程及研讨会，涵盖实验方法与理论分析。
In a recent paper (hep-ph/0608271) we describe a new approach to rapidity gap survival (RGS) in the production of high-mass systems (H = dijet, Higgs, etc.) in exclusive double-gap diffractive pp scattering, pp -> p + H + p. It is based on the idea that hard and soft interactions are approximately independent (QCD factorization), and allows us to calculate the RGS probability in a model-independent way in terms of the gluon generalized parton distributions (GPDs) in the colliding protons and the pp elastic scattering amplitude. Here we focus on the transverse momentum dependence of the cross s…
Transverse force tomography inside a proton from Basis Light-front Quantization
研究通过轻前端波函数探讨横向极化质子内部的横向力，揭示其与Sivers不对称性的关系，并在正向极限下提取扭力-3减少矩阵元。
We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization an…
We present a short overview on the studies of transverse momentum dependent parton distribution functions of the nucleon. The aim of such studies is to provide a three dimensional imagining of the nucleon and a comprehensive description of semi-inclusive high energy reactions. By comparing with the theoretical framework that we have for the inclusive deep inelastic lepton-nucleon scattering and the one-dimensional imaging of the nucleon, we summarize what we need to do in order to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three dimensional ga…
Transverse force distributions in the proton from lattice QCD
针对极化深度非弹性散射中单自旋不对称性的夸克层面理解问题，本文通过格点QCD计算质子中被撞击夸克所受色-洛伦兹力的空间分布，确定了自旋无关禁闭力及约3 GeV/fm的自旋相关局域力分布，为Sivers不对称性提供互补图像。
We discuss several examples of how the transverse spatial distribution of partons in the nucleon, as well as multiparton correlations, can be probed by observing hard processes (dijets) in high-energy pp (pbar p) and pA (dA) collisions. Such studies can complement the information gained from measurements of hard exclusive processes in ep scattering. The transverse spatial distribution of partons determines the distribution over pp impact parameters of events with hard dijet production. Correlations in the transverse positions of partons can be studied in multiple dijet production. We find that…
Transverse force distributions in the proton from lattice QCD
基于格点 QCD 计算，研究了质子中作用于被击中夸克的色-洛伦兹力横向空间分布，揭示了自旋无关与自旋相关的力分布，为 Sivers 不对称性提供了新视角。
Color Lorentz force on a transversely polarized quark in the nucleon
该研究关联未极化标量部分子分布函数的高 twist 分量矩与核子内夸克的横向色洛伦兹力，通过 Basis Light-Front Quantization 框架计算形状因子，揭示 Boer--Mulders 力的空间图像。
We calculate the static potential, the drag force and the jet quenching parameter in strongly coupled anisotropic N=4 super Yang-Mills plasma. We find that the jet quenching is in general enhanced in presence of anisotropy compared to the isotropic case and that its value depends strongly on the direction of the moving quark and the direction along which the momentum broadening occurs. The jet quenching is strongly enhanced for a quark moving along the anisotropic direction and momentum broadening happens along the transverse one. The parameter gets lower for a quark moving along the transvers…
Imaging baryon number density within the proton
研究通过光子-质子碰撞产生介子通道，探测质子内部宇称电荷分布，发现其横向半径为0.33-0.53 fm，且集中在质子中心。
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