<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math> meson generalized parton distributions in the Nambu–Jona-Lasinio model
Jin-Li Zhang, Guang-Zhen Kang, Jialun Ping
Abstract
In this paper, both the unpolarized and the polarized $\ensuremath{\rho}$ meson generalized parton distributions are investigated in the framework of the Nambu--Jona-Lasinio model using the proper time regularization scheme. The symmetry properties of $\ensuremath{\rho}$ 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 ${\stackrel{\texttildelow{}}{F}}_{1}^{u}(t)$ and ${\stackrel{\texttildelow{}}{F}}_{2}^{u}(t)$ 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 $\ensuremath{\rho}$ meson generalized parton distributions satisfy the required properties well.