Parity Doubling and the Dense Matter Phase Diagram under Constraints from Multi-Messenger Astronomy

We extend the recently developed hybrid quark-meson-nucleon model by augmenting a six-point scalar interaction and investigate the consequences for neutron-star sequences in the mass-radius diagram. The model has the characteristic feature that, at increasing baryon density, the chiral symmetry is restored within the hadronic phase by lifting the mass splitting between chiral partner states (parity doubling), before quark deconfinement takes place. At low temperature and finite baryon density, the model predicts a first-, second-order chiral phase transition, or a crossover, depending on the expectation value of the scalar field, and a first-order deconfinement phase transition. We discuss two sets of free parameters, which result in compact-star mass-radius relations that are at tension with the combined constraints for maximum-mass ($2~M_\odot$) and the compactness (GW170817). We find that the most preferable mass-radius relations result in isospin-symmetric phase diagram with rather low temperature for the critical point of the chiral phase transition.