Chiral Phase Structure and In-Medium Modifications of Charmed Meson Masses within SU(4) extended Linear-Sigma Models

Abstract

We extend the Polyakov-loop-enhanced linear-sigma model to encompass four flavors and utilize it to analyze the light, strange, and charmed meson mass spectrum as it transitions from the vacuum into a hot and dense medium. Within the mean-field approximation, we determine the masses of scalar ($0^{++}$), pseudoscalar ($0^{-+}$), vector ($1^{--}$), and axial-vector ($1^{++}$) meson states, encompassing both open- and hidden-charm constituents, as functions of temperature $T$ and baryon chemical potential $μ_B$. With parameters calibrated to the vacuum spectrum, the charm degree of freedom proves essential for an accurate description of observed masses, and charmed states acquire their in-medium modifications from the light and strange condensates that modify their valence quarks. Each species seems to undergo melting along its distinct trajectory, yet all transitions occur within a narrow band surrounding the chiral transition. The open-charm $D$-meson functions as a precise indicator of chiral restoration: its mass increases substantially across the transition and reflects the non-strange condensate, whereas hidden-charm states remain largely unaffected and serve as reference standards for the surrounding matter. We establish that transition points from three independent measurements delineate the chiral phase boundary ($T_c$, $μ_B$), whose curvature matches lattice-QCD predictions and which persists as a crossover throughout the examined range, exhibiting no critical endpoint.