$\rho$ meson generalized parton distributions in the Nambu--Jona-Lasinio model

TL;DR

This paper investigates the unpolarized and polarized $ ho$ meson generalized parton distributions within the Nambu--Jona-Lasinio model, providing insights into their properties, form factors, and impact parameter distributions.

Contribution

It presents a comprehensive calculation of $ ho$ meson GPDs and related form factors using the NJL model with proper time regularization, including symmetry checks and impact parameter analysis.

Findings

Obtained $ ho$ meson form factors $G_C(t)$, $G_M(t)$, $G_Q(t)$.

Calculated polarized and unpolarized GPDs consistent with theoretical properties.

Studied impact parameter dependent distributions revealing spatial structure.

Abstract

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.