Dynamical Mass and the Equation of State in a Quarkyonic Parity Doublet Framework

We develop a unified framework for dense symmetric nuclear matter by combining the quarkyonic matter description with the parity doublet model (PDM). In this approach, both nucleons and constituent quarks possess a chiral invariant mass, enabling a smooth crossover from hadronic to quark degrees of freedom while incorporating chiral symmetry restoration. The nucleon and constituent quark masses decrease with increasing density, reflecting the partial restoration of chiral symmetry. We find that this density-dependent mass treatment yields a stiffer equation of state and larger sound velocity compared to the conventional quarkyonic model with constant masses. The sound velocity shows sensitivity to the invariant mass component of the constituent quark: a smaller invariant mass fraction leads to larger sound velocity values, analogous to the behavior found in the original PDM analysis.