Chiral invariant mass and scale symmetry in dense matter from a dilaton compensated parity doublet model

Abstract

In the parity doublet model the nucleon mass includes a chiral invariant part $m_0$, which is conventionally assumed to be medium independent. We promote this assumption to a dynamical question by making the model scale invariant using a dilaton compensator $χ$, so that the effective chiral invariant mass $m_{\rm inv}^\ast = m_0\tildeχ$, with $\tildeχ= χ/f_χ$, responds to the partial restoration of scale symmetry in the medium. We fit the model parameters by using vacuum spectra, nuclear matter properties, and NICER mass--radius posteriors---with the hadronic equation of state connected to 2+1-flavor Nambu--Jona-Lasinio quark matter by an interpolation. The best fit gives $m_0 = 657$ MeV, a maximum neutron-star mass of $2.30\,M_\odot$ and $R_{1.4} = 12.22$ km, with the mass--radius sequence passing through all three NICER credible regions. The resulting tidal deformabilities, $Λ_{1.4} = 387$ and $\tildeΛ= 463$, are consistent with GW170817 measurements. The in-medium analysis separates the two restorations: at the hadron--quark matching density the chiral condensate falls to $56\%$ of its vacuum value, while the dilaton decreases only to $94\%$, so the nucleon arrives at the matching density with $90\%$ of its mass carried by the invariant part. The order parameters of chiral and scale symmetries organize the in-medium probes, making the $ω$ an almost pure probe of scale symmetry and the $ρ$ of chiral restoration, which gives us a clue on the origin of hadron mass.