On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out and QCD Critical Endpoint

We calculate the first six non-normalized moments of particle multiplicity within the framework of the hadron resonance gas model. In terms of the lower order moments and corresponding correlation functions, general expressions of higher order moments are derived. Thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials {\mu}, so that it is possible to evaluate them at chemical freeze out curve. It is found that a non-monotonic behavior, reflecting the dynamical fluctuation and strong correlation of particles starts to appear from the normalized third order moment. We introduce novel conditions for describing the chemical freeze out curve. Although the hadron resonance gas model does not contain any information on the criticality related to the chiral dynamics and singularity in some physical observables, we are able find out the location of the QCD critical endpoint at $\mu\sim 350 $MeV and temperature $T \sim 162 $MeV.