Meson fluctuations and thermodynamics of the Polyakov-loop-extended quark-meson model

Thermodynamics of the Polyakov-loop-extended two-flavor chiral quark-meson model (PQM) is explored. The analysis of the PQM model is based on the functional renormalization group method. An appropriate truncation of the effective action with quarks coupled to background gluonic fields is introduced. Within this scheme, we derive the renormalization group flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry breaking external field. The influence of fluctuations and of the background gluon field on the properties of net-quark number density fluctuations and their higher moments is explored. We study the dependence of the kurtosis of quark-number fluctuations on the pion mass and show that, in the presence of a symmetry-breaking term, the fluctuations lead to a smoothing of observables near the crossover transition.