  Higher moments of event-by-event net-proton multiplicity distributions are
applied to search for the QCD critical point in the heavy ion collisions. It
has been demonstrated that higher moments as well as moment products are
sensitive to the correlation length and directly connected to the thermodynamic
susceptibilities computed in the Lattice QCD and Hadron Resonance Gas (HRG)
model. In this paper, we will present measurements for kurtosis ($\kappa$),
skewness ($S$) and variance ($\sigma^{2}$) of net-proton multiplicity
distributions at the mid-rapidity ($|y|<0.5$) and $0.4<p_{T}<0.8$ GeV/$c$ for
Au+Au collisions at $\sqrt{s_{NN}}$=19.6, 39, 62.4, 130 and 200 GeV, Cu+Cu
collisions at $\sqrt{s_{NN}}$=22.4, 62.4 and 200 GeV, d+Au collisions at
$\sqrt{s_{NN}}$=200 GeV and p+p collisions at $\sqrt{s_{NN}}$=62.4 and 200 GeV.
The moment products $\kappa \sigma^{2}$ and $S \sigma$ of net-proton
distributions, which are related to volume independent baryon number
susceptibility ratio, are compared to the Lattice QCD and HRG model
calculations. The $\kappa \sigma^{2}$ and $S \sigma$ of net-proton
distributions are consistent with Lattice QCD and HRG model calculations at
high energy, which support the thermalization of the colliding system.
Deviations of $\kappa \sigma^{2}$ and $S \sigma$ for the Au+Au collisions at
low energies from HRG model calculations are also observed.
