Investigation of the nuetralino pair production at LHC

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.