Spectroscopy of $\rho$-meson in symmetric nuclear medium

In this work, we investigate the behavior of the light vector $\rho$ meson in the presence of a symmetric nuclear medium at zero temperature. We calculate the mass and decay constant of the $\rho$-meson as well as the leading twist distribution amplitudes (DAs) in the light-front quark model in vacuum, which are further investigated at different baryonic densities. We also predict the Mellin moments of the DAs and decay width of the $\rho^0 \to e^+ e^-$ process in both vacuum and medium. The evolution of DAs is carried out by the leading order (LO) Efremov-Radyushkin-Brodsky-Lepage method and compared with available predictions. For better understanding of medium effects on $\rho$-meson, we have also predicted the in-medium charge ($G_C(Q^2)$), magnetic ($G_M(Q^2)$), and quadrupole ($G_Q(Q^2)$) form factors. The in-medium charge radii, magnetic moment, and quadrupole moment have also been predicted in this work. We have found that the nuclear medium induces appreciable modifications on the mass, weak decay constant, decay width, and distribution amplitudes of the $\rho$ meson. However, the charge radii, magnetic moment, and quadrupole moment are observed to exhibit weaker sensitivity to changes in baryonic density.