Pair ${(bc)}$ diquarks production in high energy proton--proton collisions

The cross section of pair double heavy diquark production process $pp\to(bc)+(\bar b \bar c)+X$ is calculated in the leading order of gluonic fusion channel with all four possible color and spin combinations $[^1S_0]_{\bar3}$, $[^1S_0]_{6}$, $[^3S_1]_{\bar3}$, and $[^3S_1]_{6}$ for each of the two final diquarks taken into account. Several sources of relativistic corrections to the cross section are handled in the framework of relativistic quark model. Perturbative $\mathcal O(v^2)$ corrections originating from the production amplitude expansions in heavy quark relative velocity~$v$ depend on the color and spin states of the final particles, but can be generally considered as unimportant ones giving maximally 12\% improvement in numerically significant cases. Modifications of the quark--quark and antiquark--antiquark bound state wave functions caused by the appropriate generalization of the Breit interaction potential have rather severe impact on the cross section suppressing it almost three times. Under assumption of antitriplets and sextuplets' nonperturbative parameters having the same order of magnitude, it is shown that the color-sextet mechanism strongly dominates pair diquark production in both nonrelativistic and relativistic approximations.