Possibility of $ \rho$ meson condensation in neutron stars: 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. We observe that the condition of $ \rho$ meson condensation is satisfied for the density of about 7$ \rho_{{0}}^{}$ , where $ \rho_{{0}}^{}$ is the nuclear saturation density. We also observe that the medium modified mass of $ \rho$ meson is found to have a considerable effect on the mass-radius relationship of neutron star. In the end, a brief qualitative discussion of the magnetic field is also involved to search for further possibilities of $ \rho$ meson condensation.