Impact Parameter 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.

ρ meson generalized parton distributions in the Nambu–Jona-Lasinio model

In this paper, both the unpolarized and the polarized $\rho$ meson generalized parton distributions are investigated in the framework of the Nambu--Jona-Lasinio model using proper time regularization scheme. The symmetry properties of $\rho$ meson generalized parton distributions are checked. The three independent distribution functions in deep inelastic scattering, $F_1(x)$, $b_1(x)$ and $g_1(x)$, and the Sachs-like charge, magnetic, and quadruple form factors $G_C(t)$, $G_M(t)$ and $G_Q(t)$, which are the first Mellin moments of unpolarized generalized parton distributions are obtained. In addition, the $u$ quark axial vector form factors $\tilde{F}_1^u(t)$ and $\tilde{F}_2^u(t)$ related to the axial currents from the polarized generalized parton distributions are studied. The impact parameter dependent parton distribution functions, which are the two-dimensional Fourier transform of generalized parton distributions are studied, too. The obtained $\rho$ meson generalized parton distributions satisfy the required properties well.

Determination of generalized parton distributions through a simultaneous analysis of axial form factor and wide-angle Compton scattering data

In this work, we present a new set of unpolarized ($ H $) and polarized ($\widetilde{H}$) generalized parton distributions (GPDs) that have been determined using a simultaneous $ \chi^2 $ analysis of the nucleon axial form factor (AFF) and wide-angle Compton scattering (WACS) experimental data at the next-to-leading order (NLO) accuracy in QCD. We explore various Ansatzes presented in the literature for GPDs, which use forward parton distributions as input, and choose the ones most suited to our analysis. The experimental data included in our analysis cover a wide range of the squared transverse momentum, which is $ 0.025 < -t < 6.46 $ GeV$ ^2 $. We show that the WACS data affect significantly the large $-t$ behavior of $\widetilde{H}$. The polarized GPDs obtained from the simultaneous analysis of AFF and WACS data differ considerably from the corresponding ones obtained by analyzing AFF and WACS separately, and have less uncertainties. We show that the theoretical predictions obtained using our GPDs are in good agreement with the analyzed AFF and WACS data for the entire range of $ -t $ studied. Finally, we obtain the impact parameter dependent parton distributions, both in an unpolarized and in a transversely polarized proton, and present them as tomography plots.

Transverse densities and generalized parton distributions of the ρ meson in the light front quark model

We have investigated the transverse charge density for longitudinal and transversely polarized $\rho$ meson in light-front quark model (LFQM). Charge densities are obtained from the elastic form factors of the $\rho$ meson calculated in LFQM including the zero-mode contributions. We have computed the different helicity matrix elements of the $\rho$ meson. In addition to this, we have also presented the results for the generalized parton distributions (GPDs) and impact-parameter dependent parton distribution functions (ipdpdfs) of the $\rho$ meson.

ρ meson GPDs and IPDs with a light-front constituent quark model

We investigate the ρ meson unpolarized Generalized Parton Distributions based on a Light-Front Constituent Quark Model. Moreover, by employing a Gaussian form wave packet, we apply the obtained generalized parton distributions to get the Impact Parameter dependent parton Distributions.

Generalized parton distributions of pion for non-zero skewness in AdS/QCD

We study the generalized parton distributions (GPDs) of pion for non-zero skewness by considering the leading |qq¯〉 Fock state component. Inspired from AdS/QCD light-front wave functions, we calculate the pion GPDs. By taking the Fourier transforms we obtain the results for impact-parameter dependent parton distribution functions (ipdpdf) and for GPDs in longitudinal boost-invariant space. We also calculate the charge density and gravitational form factor of the pion. The pion unpolarized transverse momentum distribution (TMD) have also been calculated. The results provide rich information on the internal structure of pion.

Meson impact parameter distributions**Supported by National Natural Science Foundation of China (11475192), the fund provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” project by the NSFC (11621131001) and the Key Research Program of Frontier Sciences, CAS (Y7292610K1)

In this paper, the meson impact parameter dependent parton distributions and the impact parameter dependent form factors are introduced and discussed. By employing a Gaussian form wave packet, we calculate the impact parameter distributions of the meson based on a light-cone constituent quark model.

Transverse (spin) structure of hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark–gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark–gluon correlations embodied in the polarized structure function g2 can be understood in terms of the proton and neutron anomalous magnetic moments.

Generalized Parton Distributions for the Proton in Position Space

We present a study of impact parameter dependent parton distributions (ipdpdfs) using a recent parametrization of u and d quark GPDs H(x,t) and E(x,t) at zero skewness ζ = 0 and discuss the region of validity of the positivity condition which puts limits on the range of x and impact parameter b⊥ used in this parametrization. We also present the GPDs in transverse and longitudinal position space using the same parametrization for non-zero ζ. For GPDs in longitudinal position space in the kinematical region x > ζ, a diffraction pattern is observed, as seen before in several other models.

Transverse (Spin) Structure of Hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark-gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for $u$ and $d$ quarks, as well as the signs of quark-gluon correlations embodied in the polarized structure function $g_2$ can be understood in terms of the proton and neutron anomalous magnetic moments.

Parton distributions in impact parameter space

The Fourier transform of the generalized parton distributions (GPDs) at zero skewness with respect to the transverse momentum transfer gives the distribution of partons in the impact parameter space. We investigate the GPDs as well as the impact parameter dependent parton distributions (ipdpdfs) by expressing them in terms of overlaps of light-front wave functions (LFWFs) and present a comparative study using three different model LFWFs.

Transverse deformation of parton distributions and transversity decomposition of angular momentum

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the $T$-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be connected with Ji's quark angular momentum relation. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd generalized parton distributions (GPDs). This result is used to provide a decomposition of the quark angular momentum with respect to (w.r.t.) quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.

Impact Parameter-Dependent Parton Distributions for a Relativistic Composite System

We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We express them in terms of overlaps of light-cone wave functions for a self consistent two-body spin-1/2 state, namely an electron dressed with a photon in QED. The pdfs are distorted in the transverse space for transverse polarization of the state at one loop level.

Impact parameter dependent parton distributions for a relativistic composite system

We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We take an effective two-body spin-1/2 state, namely an electron dressed with a photon in QED. We express the impact parameter dependent parton distributions in terms of overlaps of light-cone wave functions. We obtain the scale dependence of both fermion and gauge boson distributions and show the distortion of the pdfs in the transverse space for transverse polarization of the state at one loop level.

Chromodynamic lensing and transverse single spin asymmetries

We illustrate, in a simple physical picture, how an axial asymmetry in impact parameter dependent parton distributions, in combination with final state interactions, can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. We also explain the correlation between the sign of the anomalous magnetic moment and the sign of the Sivers asymmetry.

IMPACT PARAMETER SPACE INTERPRETATION FOR GENERALIZED PARTON DISTRIBUTIONS

The Fourier transform of generalized parton distribution functions at ξ = 0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to impact parameter distribution of unpolarized quarks for an unpolarized nucleon, [Formula: see text] is related to the distribution of longitudinally polarized quarks in a longitudinally polarized nucleon, and E is related to the distortion of the unpolarized quark distribution in the transverse plane when the nucleon has transverse polarization. The magnitude of the resulting transverse flavor dipole moment can be related to the anomalous magnetic moment for that flavor in a model independent way.