Charmed Meson Structure across Crossover from SU($4$) Polyakov Quark Meson Model with Isospin Asymmetry

The Polyakov Quark Meson (PQM) model is extended to SU($4$) flavor symmetry by incorporating the charm quark and introducing a finite isospin asymmetry. This model incorporates the light, strange, and charm chiral condensates, along with the Polyakov-loop variables, to describe the confinement--deconfinement phase transition in a thermal and dense QCD medium. The inclusion of the charm quark condensate enhances the capability of the SU($4$) PQM model to explore the spatial and thermal resolution of the chiral phase structure, particularly in the crossover and high-temperature regimes. We construct the QCD phase diagram (T/T_χ-μI/m_π) plane, indicating a decrease in the pseudo-critical temperature as the isospin chemical potential increases and explore thermodynamic quantities related to the QCD equation of state at very high temperatures. Fluctuations of quark flavors, conserved charges and baryon-charm correlations are studied across a wide temperature range. The SU($4$) PQM model exhibits good qualitative agreement with lattice QCD calculations. Additionally, we calculate the meson mass spectrum at zero and finite temperature, showing that the charm sector remains thermally stable over a wide temperature range. Overall, this study highlights the capability of the SU($4$) PQM model to describe key features of QCD matter at high temperatures and its relevance to heavy-ion collisions and astrophysical studies. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.