Polyakov linear-σ model in mean-field approximation and optimized perturbation theory

The optimized perturbation theory (OPT) is confronted to first-principle lattice simulations. We compare results from the Polyakov linear-sigma model (PLSM) in OPT with the conventional mean-field approximation (MFA). At finite temperatures and chemical potentials, the chiral condensates and the decofinement order parameters, the thermodynamic pressure, the pseudocritical temperatures, the subtracted condensates, the second- and high-order moments of various conserved charges (cumulants) obtained in MFA are compared with OPT and also confronted to available lattice quantum chromodynamics (QCD) simulations. We conclude that when moving from lower- to higher-order moments of different quantum charges, OPT becomes more closer to lattice QCD simulations. The higher-order moments of conserved charges, such as baryon, strange, and electric charge, are proportional to powers of the correlation length and thus expected to diverge at the critical endpoint of the QCD phase boundary.Making sure that one approximate approach is more sensitive than another, even slightly, is crucial for implementing PLSM, for instance, in positioning critical endpoint and providing an important signature for the possible experimental detection. © 2020 American Physical Society. All rights reserved.