Generalized Transverse-momentum Dependent Parton Distributions Research Articles

Gluon GTMDs at nonzero skewness and impact parameter dependent parton distributions

We investigate the leading twist generalized transverse momentum dependent parton distributions (GTMDs) of the unpolarized and longitudinally polarized gluons in the nucleon. We adopt a light-front gluon-triquark model for the nucleon motivated by soft-wall AdS/QCD. The gluon GTMDs are defined through the off-forward gluon-gluon generalized correlator and are expressed as the overlap of light-cone wave functions. The GTMDs can be employed to provide the generalized parton distributions (GPDs) by integrating out the transverse momentum. The Fourier transform of the GPDs encodes the parton distributions in the transverse position space, namely, the impact parameter dependent parton distributions (IPDs). We also calculate the three gluon IPDs corresponding to the GPDs Hg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^g$$\\end{document}, Eg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E^g$$\\end{document} and H~g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{H}^g$$\\end{document}, and present their dependence on x and b⊥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_\\perp $$\\end{document}, respectively.

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Exploring twist-4 chiral-even GPDs in the light-front quark-diquark model

In this work, we delve into the realm of quantum chromodynamics (QCD) by calculating twist-4 chiral-even generalized parton distributions (GPDs), within the context of the light-front quark-diquark model (LFQDM), focusing specifically on the intriguing case of zero skewness. To shed light on the behavior of twist-4 chiral-even GPDs, we present comprehensive two-dimensional (2-D) and 3-dimensional (3-D) plots, mapping their dependence on the longitudinal momentum fraction (x) and the momentum transfer (t). Furthermore, our research looks into the profound connection between twist-4 chiral-even GPDs and other distribution functions (DFs), including parton distribution functions (PDFs), transverse momentum-dependent parton distributions (TMDs) and generalized transverse-momentum dependent parton distributions (GTMDs). Additionally, our investigation extends to the exploration of related higher twist form factors (FFs), which play a pivotal role in elucidating the internal structure of hadrons. To provide significant insights into the partons spatial distribution, we have also yielded impact parameter GPD plots.

Exclusive double quarkonium production and generalized TMDs of gluons

Being the “mother distributions” of all types of two-parton correlation functions, generalized transverse momentum dependent parton distributions (GTMDs) have attracted a lot of attention over the last years. We argue that exclusive double production of pseudoscalar quarkonia (ηc or ηb) in nucleon-nucleon collisions gives access to GTMDs of gluons.

From Ji to Jaffe-Manohar orbital angular momentum in lattice QCD using a direct derivative method

A Lattice QCD approach to quark orbital angular momentum in the proton based on generalized transverse momentum-dependent parton distributions (GTMDs) is enhanced methodologically by incorporating a direct derivative technique. This improvement removes a significant numerical bias that had been seen to afflict results of a previous study. In particular, the value obtained for Ji quark orbital angular momentum is reconciled with the one obtained independently via Ji's sum rule, validating the GMTD approach. Since GTMDs simultaneously contain information about the quark impact parameter and transverse momentum, they permit a direct evaluation of the cross product of the latter. They are defined through proton matrix elements of a quark bilocal operator containing a Wilson line; the choice in Wilson line path allows one to continuously interpolate from Ji to Jaffe-Manohar quark orbital angular momentum. The latter is seen to be significantly enhanced in magnitude compared to Ji quark orbital angular momentum, confirming previous results.

T-odd generalized and quasi transverse momentum dependent parton distribution in a scalar spectator model

Generalized transverse momentum dependent parton distributions (GTMDs), as mother funtions of transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs), encode the most general parton structure of hadrons. We calculate four twist-two time reversal odd GTMDs of pion in a scalar spectator model. We study the dependence of GTMDs on the longitudinal momentum fraction x carried by the active quark and the transverse momentum |vec k_T| for different values of skewness xi defined as the longitudinal momentum transferred to the pion as well as the total momentum |vec Delta _T| transferred to the pion. In addition, the quasi-TMDs and quasi-GPDs of pion have also been investigated in this paper.

Sivers and Boer–Mulders GTMDs in light-front holographic quark–diquark model

We calculate the time reversal odd (T-odd) generalized transverse momentum dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We have incorporated both scalar and axial vector diquarks in the model and obtained an overlap representation of the GTMDs using the light-front wave functions (LFWFs). Contribution from the final state interaction is incorporated at the level of one gluon exchange as a phase factor in the LFWF. We show that the final state interaction term can be factored out in this model and this part is the same for both GTMDs. We also present the corresponding Wigner distributions.

Study of kaon structure using the light-cone quark model

We investigate the various distributions explaining multi-dimensional structure of kaon at the level of its constituents ($u$ and $\bar{s}$) using the light-cone quark model. The overlap form of wavefunctions associated with the light-cone quark model is adopted for the calculations. The generalized parton distributions(GPDs)of $u$ and $\bar{s}$ quarks are presented for the case when the momentum transfer in the longitudinal direction is non-zero. The dependence of kaon GPDs is studied in terms of variation of quark longitudinal momentum fraction, momentum transfer in longitudinal direction and total momentum transfer to the final state of hadron. The transverse impact-parameter dependent GPDs are also studied by taking the Fourier transformation of general GPDs. Further, the quantum phase-space distributions; Wigner distributions are studied for the case of unpolarized, longitudinally-polarized and transversely-polarized parton in an unpolarized kaon. The Wigner distributions are analysed in the transverse impact-parameter plane, the transverse momentum plane and the mixed plane. Further, to get a complete picture of kaon in terms of its valence quarks, the variation of longitudinal momentum fraction carried by quark and antiquark in the generalized transverse momentum-dependent parton distributions (GTMDs) is studied for different values of transverse quark and antiquark momentum $({\bf k}_\perp)$ as well as for different values of momentum transferred to the kaon in transverse direction $({\bf \Delta}_\perp)$. This has been done for zero as well as non-zero skewedness representing respectively the absence and presence of momentum transfer to the final state of kaon in longitudinal direction. Furthermore, the possible spin-orbit correlation for $u$ and $\bar{s}$ in kaon is elaborated in context of Wigner distributions and GTMDs.

Generalized TMDs and the exclusive double Drell–Yan process

Generalized transverse momentum dependent parton distributions (GTMDs) are the most general parton correlation functions of hadrons. By considering the exclusive double Drell–Yan process it is shown for the first time how quark GTMDs can be measured. Specific GTMDs can be addressed by means of polarization observables.

Generalized TMDs

Generalized transverse-momentum dependent parton distributions (GTMDs) encode the most general parton structure of hadrons. In this contribution, which is largely based on a recent publication,1 we focus on two twist-2 GTMDs which are denoted by F1,4 and G1,1 in parts of the literature. As already shown previously, both GTMDs have a close relation to orbital angular momentum of partons inside a hadron. However, recently even the mere existence of F1,4 and G1,1 has been doubted. We explain why this claim does not hold. We support our model-independent considerations by calculating the GTMDs in two spectator models and in perturbative QCD. For the model results we also explicitly check the relation to the orbital angular momentum of partons inside hadrons.

Twist-2 generalized transverse-momentum dependent parton distributions and the spin/orbital structure of the nucleon

Generalized transverse-momentum dependent parton distributions (GTMDs) encode the most general parton structure of hadrons. Here we focus on two twist-2 GTMDs which are denoted by $F_{1,4}$ and $G_{1,1}$ in parts of the literature. As already shown previously, both GTMDs have a close relation to orbital angular momentum of partons inside a hadron. However, recently even the mere existence of $F_{1,4}$ and $G_{1,1}$ has been doubted. We explain why this claim does not hold. We support our model-independent considerations by calculating the two GTMDs in the scalar diquark model and in the quark-target model, where we also explicitly check the relation to orbital angular momentum. In addition, we compute $F_{1,4}$ and $G_{1,1}$ at large transverse momentum in perturbative Quantum Chromodynamics and show that they are nonzero.

Quark Wigner distributions and orbital angular momentum

We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse-momentum dependent parton distributions. They depend on both the transverse position and the three-momentum of the quark relative to the nucleon, and therefore combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. We focus the discussion on the distributions of unpolarized/longitudinally polarized quark in an unpolarized/longitudinally polarized nucleon. In this way, we can study the role of the orbital angular momentum of the quark in shaping the nucleon and its correlations with the quark and nucleon polarizations. The quark orbital angular momentum is also calculated from its phase-space average weighted with the Wigner distribution of unpolarized quarks in a longitudinally polarized nucleon. The corresponding results obtained within different light-cone quark models are compared with alternative definitions of the quark orbital angular momentum, as given in terms of generalized parton distributions and transverse-momentum dependent parton distributions.

Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon

We present a systematic study of generalized transverse-momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. We present such simultaneous modeling by considering a light-cone wave function overlap representation of the GTMDs. We construct the different quark-quark correlation functions from the 3-quark Fock components within both the light-front constituent quark model as well as within the chiral quark-soliton model. We provide a comparison with available data and make predictions for different observables.