Evidence for a Continuous Hadron--Quark Transition in Cold Dense Matter

Abstract

Statistical evidence for a continuous hadron-quark transition is found in this work. Confronting microscopic descriptions connecting the Parity Doublet Model and the Nambu--Jona-Lasinio model with observationally constrained non-parametric equations of state, Bayesian model comparison decisively favors a boundary-free crossover over the conventional first-order Maxwell construction ($\Delta \ln \mathcal{Z}\sim +7.20$) and fixed-boundary crossover ($\Delta \ln \mathcal{Z}\sim +5.16$). The preferred crossover decouples the intermediate stiffening from the intrinsic stiffness of each phase, allowing both sectors to exhibit physical self-consistency. The chiral-invariant nucleon mass is large, $M_0=834_{-92}^{+28}\text{ MeV}$, as expected for a substantial baryon mass surviving chiral restoration. While the quark sector accommodates a small pairing gap ${\Delta }_{\mathrm{CFL}}=88_{-59}^{+83}\text{ MeV}$ consistent with perturbative QCD limits, avoiding the excessively large gaps ${\Delta }_{\mathrm{CFL}}\gtrsim 200\text{ MeV}$ required by the other constructions. These results demonstrate that a realistic unified description represents a continuous transition deviating substantially from isolated effective models of hadrons and quarks. Exploring genuine phase boundaries is therefore necessary through the emergence of spinodal instabilities within unified frameworks.

Comments: 5+8 pages, 4+3 figures