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The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density

Thermodynamics and the phase structure of the Polyakov loop-extended two flavors chiral quark--meson (PQM) model is explored beyond the mean-field approximation. The analysis of the PQM model is based on the functional renormalization group (FRG) method. We formulate and solve the renormalization group flow equation for the scale-dependent thermodynamic potential in the presence of the gluonic background field at finite temperature and density. We determine the phase diagram of the PQM model in the FRG approach and discuss its modification in comparison with the one obtained under the mean-field approximation. We focus on properties of the net-quark number density fluctuations as well as their higher moments and discuss the influence of non-perturbative effects on their properties near the chiral crossover transition. We show, that with an increasing net-quark number density the higher order moments exhibit a peculiar structure near the phase transition. We also consider ratios of different moments of the net-quark number density and discuss their role as probes of deconfinement and chiral phase transitions.