Transverse momentum dependent parton distributions in a light-cone quark model

TL;DR

This work develops a light-cone quark-model (LCQM) framework truncated to the valence three-quark sector to derive analytic overlap representations for leading-twist TMDs. By employing six LCWF amplitudes generated via Melosh rotations under SU(6) symmetry, it yields explicit expressions and relations among TMDs, revealing that only three T-even TMDs are independent in this truncation. Numerical results with a power-law momentum wave function show non-Gaussian k_perp dependence, sizable pretzelosity, and a strong link between relativistic spin-orbit effects and nucleon deformation, underscoring the role of orbital angular momentum in shaping TMDs. The study also emphasizes model dependence and highlights density-shape implications for SIDIS/DY phenomenology, while acknowledging the absence of gluonic degrees of freedom in the current setup.

Abstract

The leading twist transverse momentum dependent parton distributions (TMDs) are studied in a light-cone description of the nucleon where the Fock expansion is truncated to consider only valence quarks. General analytic expressions are derived in terms of the six amplitudes needed to describe the three-quark sector of the nucleon light-cone wave function. Numerical calculations for the T-even TMDs are presented in a light-cone constituent quark model, and the role of the so-called pretzelosity is investigated to produce a nonspherical shape of the nucleon.

Figures (9)

• Figure 1: (Color online) The TMDs $f_1$, $g_{1L}$, $h_1$ as functions of $x$ and $\boldsymbol{k}^2_\perp$ are shown in the upper, middle and lower panels, respectively. Results for up and down quarks are given in the left (right) panels.
• Figure 2: (Color online) The TMDs $h_{1L}$ and $h_{1T}^\perp$ as functions of $x$ and $\boldsymbol{k}^2_\perp$ are shown in the upper and lower panels, respectively. Results for up and down quarks are given in the left (right) panels.
• Figure 3: (Color online) The contribution to the TMD $h_{1T}^{u\perp}$ from the $L_z=\pm 1$ wave components (left panel) and (right panel) from the $L_z=0$ and $L_z=2$ wave components as a function of $x$ and $\boldsymbol{k}^2_\perp$. Upper (lower) panels for up and down quarks.
• Figure 4: The parton distribution $h_{1T}^{\perp q}(x)$ (left panels) and the transverse moment $h_{1T}^{(1)\perp q}(x)$ (right panels). Solid curves: results from the light-cone CQM model with the momentum wave function of Ref. Schlumpf:94a. Dashed curves in the upper panels: results from the light-cone CQM model with the momentum wave function in the hypercentral model of Ref. FaccioliGiannini. Dashed curves in the lower panels: results from the spectator model of Ref. Mulders3. Dotted curves: results from the bag model.
• Figure 5: The transverse moments $h_{1L}^{\perp(1)\,q}$ (left panels) and $g_{1T}^{(1)\,q}$ (right panels) as functions of $x$. Upper (lower) panels for up and down quarks. Solid curves refer to the result obtained with the light-cone CQM model; dashed curves refer to the Wandzura-Wilczek-type approximation.