  We consider that the direct production of a single neutralino in
proton-proton collision at the CERN Large Hadron Collider focusing on the
lightest neutralino is possibly a candidate for the dark matter and escapes
detection. We present a comprehensive investigation of the dependence of total
cross sections of the processes $pp(q\bar
q)\rightarrow\widetilde\chi_{i}^{0}\widetilde{\text{g}}$, $pp(q \text{g})
\rightarrow\widetilde\chi_{i}^{0}\widetilde{q}_{L,R}$,
$pp(q\bar{q}^{\prime})\rightarrow\widetilde\chi_{i}^{0}\widetilde\chi_{j}^{+}$
at tree-level and
$pp(\text{g}\text{g})\rightarrow\widetilde\chi_{i}^{0}\widetilde{\text{g}}$ at
one-loop level, on the center-of-mass energy, on the $M_2$-$\mu$ mass plane, on
the squark mass and on the $\tan\beta$ for the Constrained Minimal
Supersymmetric Standard Model and the three extremely different scenarios in
the Minimal Supersymmetric Standard Model. In particular, the cross section of
the process $p p \to \widetilde\chi_{2}^{0}\widetilde\chi_{1}^{+}$ in the
gaugino-like scenario can reach about 0.6 (1.7) pb at a center-of-mass energy
of $\sqrt{s}=$ 7 (14) TeV. We derive therefrom that our results might lead to
new aspects corresponding to experimental explorations, and these dependencies
might be used as bases of experimental research of the single neutralino
production at hadron colliders.
