  In this article, we investigate the Drell-Yan process of the light neutralino
pair $\widetilde{\chi}_{i}^{0}\widetilde{\chi}_{j}^{0}$ ($i,j=1,2$) productions
at proton-proton collisions and we present the general formulate for the
differential cross sections. We conduct an extensive examination of the
dependence of the total cross section of the subprocesses $q \bar q \to
\widetilde \chi_{i}^{0}\widetilde\chi_{j}^{0}$ on the beam energy, on the mass
of the squarks and also on the $M_2$ gaugino for the three extremely different
scenarios. For all three cases, the outcomes are as follows. The dependence of
the total cross section of the subprocesses $q \bar q \to \widetilde
\chi_{i}^{0} \widetilde \chi_{j}^{0}$ on the beam energy is dominated by one of
the subprocesses, $q \bar q \to \widetilde \chi_{1}^{0} \widetilde
\chi_{2}^{0}$. On the other hand, the dependence of the total cross section of
the subprocesses $q \bar q \to \widetilde \chi_{i}^{0} \widetilde \chi_{j}^{0}$
on the mass of the squarks is dominated by one of the subprocesses, $q \bar q
\to \widetilde \chi_{1}^{0} \widetilde \chi_{2}^{0}$. We derive there from that
our findings may lead to new insights relating to experimental investigations
and these dependencies may be used as bases of an experimental research for the
neutralino pair at LHC.
