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

## TL;DR

This paper investigates the potential for $
ho$ meson condensation in neutron stars by combining chiral SU(3) models with QCD sum rules, finding it possible at high densities around 7 times nuclear saturation density.

## Contribution

It introduces a unified approach using chiral SU(3) models and QCD sum rules to assess $
ho$ meson condensation in neutron star matter, a novel combination in this context.

## Key findings

- $
ho$ meson condensation occurs at about 7$
ho_0$ density.
- Quark and gluon condensates are calculated within the chiral SU(3) model.
- Magnetic field effects are qualitatively discussed.

## 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.