Effective QCD phase diagram: parameter fixing, fluctuations, and speed of sound

The authors study the effective QCD phase diagram within the linear sigma model with quarks (LSMq), incorporating quantum and thermal corrections to the thermodynamic potential, including ring diagrams in the high-temperature regime. Model parameters are constrained by imposing a second-order chiral phase transition in the low baryon density limit, matching the curvature of the critical line from lattice QCD, and reproducing the behaviour of the speed of sound at high temperature. The authors emphasise the role of the speed of sound as a sensitive probe of the equation of state and critical dynamics. Under these constraints, the authors analyse the emergence and location of the critical end point (CEP), identifying characteristic signatures associated with rapid changes in thermodynamic observables. Finally, the authors discuss extensions toward the high-density regime and their connection with quarkyonic matter.