Toward a unified hadron-quark equation of state for neutron stars within the relativistic mean-field model

The equation of state of dense matter remains a central challenge in astrophysics and high-energy physics, particularly at supranuclear densities where exotic degrees of freedom like hyperons or deconfined quarks are expected to appear. Neutron stars provide a unique natural laboratory to probe this regime. In this work, we present EVA--01, a novel equation of state that provides a unified description of dense matter by incorporating both hadron and quark degrees of freedom within a single relativistic mean-field Lagrangian, from which the equation of state is derived at finite temperature. The model extends the density-dependent formalism by introducing a Polyakov-loop-inspired scalar field to dynamically govern the hadron-quark phase transition, following the approach of chiral mean-field models. The resulting model is consistent with a wide range of theoretical and observational constraints, including those from chiral effective field theory, massive pulsars, gravitational-wave events, and NICER data. We analyze its thermodynamic properties by constructing the QCD phase diagram, identifying the deconfinement, chiral, and nuclear liquid-gas transitions. As a first application, we model the evolution of protoneutron stars using isentropic snapshots and explore the implications of the slow stable hybrid star hypothesis. Our findings establish EVA--01 as a robust and versatile framework for exploring dense matter, bridging the gap between microphysical models and multimessenger astrophysical observations.