Strong correlation of the neutron star core-crust transition density with the $\sigma$-meson mass via vacuum polarization

We study the neutron star core-crust transition density $\rho_t$ with the inclusion of the vacuum polarization in the dielectric function in the nonlinear relativistic Hartree approach (RHAn). It is found that the strong correlation between the $\rho_{t}$ and the scalar meson mass $m_{\sigma}$ strikingly overwhelms the uncertainty of the nuclear equation of state in the RHAn models, in contrast to the usual awareness that $\rho_{t}$ is predominantly sensitive to the isovector nuclear potential and symmetry energy. The accurate extraction of $\rho_{t}$ through the future gravitational wave measurements can thus provide a strong constraint on the longstanding uncertainty of $m_{\sigma}$, which is of significance to better infer the vacuum property. As an astrophysical implication, it suggests that the correlation between $\rho_t$ and $m_\sigma$ is very favorable to reconcile the difficulty in reproducing the large crustal moment of inertia for the pulsar glitches with the well constrained symmetry energy.