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Heavy quarkonium production at high energies has provided a useful laboratory for testing the high-energy limit of quantum chromodynamics (QCD) as well as the interplay of perturbative and nonperturbative phenomena in QCD. The factorization formalism of nonrelativistic QCD (NRQCD) [4] is a theoretical framework for the description of heavy-quarkonium production and decay. The factorization hypothesis of NRQCD assumes the separation of the effects of long and short distances in heavy-quarkonium production. NRQCD is organized as a perturbative expansion in two small parameters, the strong-coupling constant αs and the relative velocity v of the heavy quarks. The phenomenology of strong interactions at high energies exhibits a dominant role of gluon interactions in quarkonium production. In the conventional parton model [5], the initial-state gluon dynamics is under the control of the Dokshitzer-Gribov-LipatovAltarelli-Parisi (DGLAP) evolution equations [6]. In this approach, it is assumed that S > μ ΛQCD, where √ S is the invariant collision energy, μ is the typical energy scale of the hard interaction, and ΛQCD is the asymptotic scale parameter. In this way, the DGLAP evolution equation takes into account only one large logarithm, namely ln(μ/ΛQCD). In fact, the collinear approximation is used, and the transverse momenta of the initial gluons are neglected. In the high-energy limit, the contribution from the partonic subprocesses involving tchannel gluon exchanges to the total cross section becomes dominant. The summation of the large logarithms ln( √ S/μ) in the evolution equation can then be more important than the one of the ln(μ/ΛQCD) terms. In this case, the non-collinear gluon dynamics is described by the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution equation [7]. In the region under consideration, the transverse momenta (kT ) of the incoming gluons and their off-shell properties can no longer be neglected, and we deal with reggeized t-channel gluons. The theoretical framework for this kind of high-energy phenomenology is the Quasi-MultiRegge-Kinematic (QMRK) approach [8], which can be based on effective quantum field theory implemented with the non-abelian gauge-invariant action, as was suggested a few years ago [9].

Heavy Quarkonium Production in the Regge Limit of QCD