Phase Stability in the 3-Dimensional Open-source Code for the Chiral mean-field Model

Abstract

In this paper we explore independently for the first time three chemical potentials (baryon ${\mu }_B$, charged ${\mu }_Q$, and strange ${\mu }_S$) in the Chiral Mean Field (CMF) model. We designed and implemented \texttt{CMF++}, a new version of the CMF model rewritten in \texttt{C++} that is optimized, modular, and well-documented. \texttt{CMF++} has been integrated into the MUSES Calculation Engine as a free and open-source software module. The runtime improved in more than 4 orders of magnitude across all 3 chemical potentials, when compared to the legacy code. Here we focus on the zero temperature case and study stable, as well as metastable and unstable, vacuum, hadronic, and quark phases, showing how phase boundaries vary with the different chemical potentials. Due to the significant numerical improvements in \texttt{CMF++}, we can now for the first time sweep the entire ${\mu }_B$, ${\mu }_S$, ${\mu }_Q$ phase space, investigate metastable phases, and calculate high-order susceptibilities within the CMF framework. This allows us to find phases of matter that include a light hadronic phase, a strangeness-dominated hadronic phase, and a quark phase. The numerical improvements also allow us to identify the order of the transitions among these phases, finding a first-order chiral symmetry restoration phase transition among the hadronic phases (favored for negative ${\mu }_Q$ and/or ${\mu }_S$ for some coupling schemes), in addition to third-order phase transitions. In particular, we identify for the first time triple points in the CMF model, where both chiral symmetry restoration and deconfinement phase transitions meet in the chemical potential phase space. Such points could potentially be identified in low-energy heavy-ion collisions.

Comments: 70 pages, 27 figures. Substantially revised and expanded version. The phase-transition classification has been refined: the point previously described as tricritical is now identified as a quantum triple point where first-order chiral-symmetry-restoration and deconfinement transitions meet. CMF++ documentation, figures, and references updated