Gravitational transverse momentum distribution of proton

Abstract

We present the first study of quark gravitational transverse-momentum distributions within the light-front quark--diquark model (LFQDM) inspired by the soft-wall AdS/QCD framework. We derive analytical expressions for the six unpolarized (T-even) gravitational transverse-momentum-dependent distributions (gravitational--TMDs) for up and down quarks within the model and compute the corresponding gravitational parton distribution functions (gravitational--PDFs). We further verify that these unpolarized gravitational--TMDs satisfy the model-independent relations with quark TMDs. In addition, we explore the connection of gravitational TMDs with the transverse isotropic pressure and shear-force distributions in momentum space, as well as with the average longitudinal momentum carried by up and down quarks within the model.

Figures (7)

• Figure 1: The gravitational transverse momentum distributions $a_{1}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{3}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{5}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{6}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{7}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, and $a_{8}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$ for the up quark, shown as functions of $x$ and $\mathbf{k}_\perp^2$ at the initial scale $\mu_0$.
• Figure 2: The gravitational transverse momentum distributions $a_{1}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{3}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{5}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{6}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{7}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, and $a_{8}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$ for the down quark, shown as functions of $x$ and $\mathbf{k}_\perp^2$ at the initial scale $\mu_0$.
• Figure 3: The unpolarized gravitational transverse-momentum distributions $a_{1}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{3}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{5}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{6}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{7}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, and $a_{8}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$ for the up quark, shown as functions of $x$ for different values of $\mathbf{k}_{\perp}^{2}$.
• Figure 4: The unpolarized gravitational transverse-momentum distributions $a_{1}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{3}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{5}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{6}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, $a_{7}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$, and $a_{8}^{(\beta)}(x,\mathbf{k}_{\perp}^{2})$ for the down quark, shown as functions of $x$ for different values of $\mathbf{k}_{\perp}^{2}$.
• Figure 5: Unpolarized gravitational parton distribution functions $A_{1}^{(\beta)}(x)$, $A_{3}^{(\beta)}(x)$, and $A_{5}^{(\beta)}(x)$ for up and down quarks, shown as functions of the momentum fraction $x$.