$\rho$ meson form factors and parton distribution functions in impact parameter space

TL;DR

This study models the $ ho$ meson's form factors and parton distributions in impact parameter space using the NJL model, comparing results with lattice data and analyzing spatial distributions of charge, magnetic, and quadrupole densities.

Contribution

It provides a detailed NJL model calculation of $ ho$ meson form factors and impact parameter space parton distributions, with comparison to lattice data and analysis of spatial extent.

Findings

Dressed form factors $G_C^D$ and $G_M^D$ agree well with lattice data.

Quadrupole form factor $G_Q^D$ is harder than lattice results.

Charge distribution range is the most extensive in impact parameter space.

Abstract

In this paper, we investigate the form factors and impact parameter space parton distribution functions of the $\rho$ meson derived from the generalized parton distributions within the framework of the Nambu--Jona-Lasinio model,employing a proper time regularization scheme. We compare the charge $G_C$, magnetic $G_M$, and quadrupole $G_Q$ form factors with lattice data. The dressed form factors, $G_C^D$ and $G_M^D$, exhibit good agreement with lattice results; however, $G_Q^D$ is found to be harder than what is observed in lattice calculations. The Rosenbluth cross section for elastic electron scattering on a spin-one particle can be expressed through the structure functions $A(Q^2)$ and $B(Q^2)$. Additionally, the tensor polarization $T_{20}(Q^2,\theta)$ can also be formulated in terms of these form factors. We analyze the structure functions $A(Q^2)$, $B(Q^2)$ and tensor polarization function $T_{20}(Q^2,\theta)$; our findings quantitatively align with predicted values across various limits. In impact parameter space, we examine parton distribution functions along with their dependence on longitudinal momentum fraction $x$ and impact parameter $\bm{b}_{\perp}$. The width distributions in impact parameter space reveal that the range of the charge distribution \( q_C(x,\bm{b}_{\perp}^2) \) is the most extensive. In contrast, the transverse magnetic radius falls within a moderate range, while the quadrupole distribution \( q_Q(x,\bm{b}_{\perp}^2) \) demonstrates the narrowest extent.