Dijet correlations at RHIC, leading-order $k_t$-factorization approach versus next-to-leading order collinear approach

We compare results of $k_t$-factorization approach and next-to-leading order collinear-factorization approach for dijet correlations in proton-proton collisions at RHIC energies. We discuss correlations in azimuthal angle as well as correlations in two-dimensional space of transverse momenta of two jets. Some $k_t$-factorization subprocesses are included for the first time in the literature. Different unintegrated gluon/parton distributions are used in the $k_t$-factorization approach. The results depend on UGDF/UPDF used. For collinear NLO case the situation depends significantly on whether we consider correlations of any two jets or correlations of leading jets only. In the first case the $2 \to 2$ contributions associated with soft radiations summed up in the $k_t$-factorization approach dominate at $\phi \sim \pi$ and at equal moduli of jet transverse momenta. The collinear NLO $2 \to 3$ contributions dominate over $k_t$-factorization cross section at small relative azimuthal angles as well as for asymmetric transverse momentum configurations. In the second case the NLO contributions vanish at small relative azimuthal angles and/or large jet transverse-momentum disbalance due to simple kinematical constraints. There are no such limitations for the $k_t$-factorization approach. All this makes the two approaches rather complementary. The role of several cuts is discussed and quantified.