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We demonstrate that the recent studies of J/psi-pair production by CMS at theLHC and by D0 at the Tevatron reveal the presence of different productionmechanisms in different kinematical regions. We find out thatnext-to-leading-order single parton scattering contributions at alpha_s^5dominate the yield at large transverse momenta of the pair. Our analysisfurther emphasises the importance of double parton scatterings --which areexpected to dominate the yield at large J/psi-rapidity differences-- at largeinvariant masses of the pair in the CMS acceptance, and thereby solve a largediscrepancy between the theory and the CMS data. In addition, we provide thefirst exact --gauge-invariant and infrared-safe-- evaluation of a class ofleading-P_T (P_T^-4) next-to-next-to-leading-order contributions at alpha_s^6,which can be relevant in the region of large values of P_T,min=min(P_T1,P_T2).Finally, we derive simple relations for the feed-down fractions from theproduction of an excited charmonium state with a J/psi in the case of thedominance of the double parton scatterings, which significantly deviate fromthose for single parton scatterings. Such relations can be used to discriminatethese extreme scenari, either DPS or SPS dominance.

J/psi-Pair Production at Large Momenta: Indications for Double-Parton Scatterings and Large alpha_s^5 Contributions