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

In the parity doublet model the nucleon mass includes a chiral invariant part m₀, 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 mᵢₙᵥ^ = m₀χ, with χ= 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 m₀ = 657 MeV, a maximum neutron-star mass of 2.30\,M_ and R1.4 = 12.22 km, with the mass--radius sequence passing through all three NICER credible regions. The resulting tidal deformabilities, Λ1.4 = 387 and Λ= 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.