  Higher moments of net-proton multiplicity distributions are applied to search
for the QCD critical point. 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 transverse
momentum range $0.4<p_{T}<0.8$ {\gevc} for Au+Au collisions at {\sNN} = 7.7,
11.5, 39, 62.4 and 200 GeV, Cu+Cu collisions at {\sNN} = 22.4, 62.4 and 200
GeV, $d$+Au collisions at {\sNN} = 200 GeV and p+p collisions at {\sNN} = 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 ratios, are consistent with Lattice QCD and Hadron Resonance Gas
(HRG) model calculations at high energies ({\sNN} = 62.4 and 200 GeV).
Deviations of $\kappa \sigma^2$ and $S\sigma$ for the Au+Au collisions at low
energies ({\sNN} = 7.7, 11.5 and 39 GeV) from HRG model calculations are also
observed.
