Chiral Phase Structure and In-Medium Modifications of Charmed Meson Masses within SU(4) extended Linear-Sigma Models
Nourhan M. Rfeek · Alexandra Friesen · Yuri Kalinovsky · Saleh O. Allehabi · Azzah A. Alshehri · Ashraf F. El-Sherif · Abdel Nasser Tawfik
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 (), pseudoscalar (), vector (), and axial-vector () meson states, encompassing both open- and hidden-charm constituents, as functions of temperature and baryon chemical potential . 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 -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 (, ), whose curvature matches lattice-QCD predictions and which persists as a crossover throughout the examined range, exhibiting no critical endpoint.