Possibility of $ρ$ Meson Condensation in Neutron Star: Unified Approach of Chiral SU(3) Model and QCD Sum Rules

Abstract: In the present work the conjunction of chiral SU(3) model with QCD sum rules is employed to explore the possibility of $\rho$ meson condensation in neutron stars. The quark and gluon condensates in terms of which the in-medium masses of $\rho$ mesons can be expressed are calculated using the chiral SU(3) model in the charge neutral matter which is relevant for neutron stars. It is observed that condition of $\rho$ meson condensation is satisfied for the density of about 7$\rho_{0}$, where $\rho_{0}$ is the nuclear saturation density. In the end, a brief qualitative discussion of the magnetic field is also involved to check out for the further possibility of $\rho$ meson condensation.