  We calculate the non-normalized moments of the particle multiplicity within
the framework of the hadron resonance gas (HRG) model. At finite chemical
potential $\mu$, a non-monotonic behavior is observed in the thermal evolution
of third order moment (skewness $S$) and the higher order ones as well. Among
others, this observation likely reflects dynamical fluctuations and strong
correlations. The signatures of non-monotonicity in the normalized fourth order
moment (kurtosis $\kappa$) and its products get very clear. Based on these
findings, we introduce a novel condition characterizing the universal
freeze-out curve. The chemical freeze-out parameters $T$ and $\mu$ are
described by vanishing $\kappa\, \sigma^2$ or equivalently $m_4=3\,\chi^2$,
where $\sigma$, $\chi$ and $m_4$ are the standard deviation, susceptibility and
fourth order moment, respectively. The fact that the HRG model is not able to
release information about criticality related to the confinement and chiral
dynamics should not veil the observations related to the chemical freeze-out.
Recent lattice QCD studies strongly advocate the main conclusion of the present
paper.
