Light-front holographic $ρ$-meson distributions in the momentum space

Abstract: We present the leading-twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 target, such as the $\rho$-meson, in the light-front framework. Specifically, we predict the TMDs in the light-front holographic model and compare with the light-front quark model predictions. We obtain the TMDs using the overlap of the light-front wave functions. We evaluate the ${\bf k}_\perp$ moments upto second order and compare with the available theoretical predictions. Further, we analyze the leading-twist parton distribution functions (PDFs) of the $\rho$-meson in the light-front holographic model which are found to be in accord with the Nambu-Jona-Lasinio (NJL) model and the light-front quark model predictions. We further study the QCD evolution of the PDFs. The positivity bounds on the TMDs and the PDFs are also discussed. We also present the quark spin densities in the transverse momentum plane for different polarization configurations of the quark and the $\rho$-meson target.