We study bottomonium hadroproduction in proton-antiproton collisions at the Fermilab Tevatron in the framework of the quasi-multi-Regge kinematics approach and the factorization formalism of nonrelativistic QCD at leading order in the strong-coupling constant s and the relative velocity v of the bound quarks. The transverse-momentum distributions of prompt nS-meson production measured at the Tevatron are fitted to obtain the nonperturbative long-distance matrix elements for different choices of unintegrated gluon distribution functions of the proton.

We study charmonium production at high-energy colliders (Tevatron, HERA, and LEP2) in the framework of the k T -factorization approach and the factorization formalism of non-relativistic quantum chromodynamics at leading order in the strong-coupling constant α s and the relative velocity v. The transverse-momentum distributions of direct and prompt J/ψ-meson production measured at the Fermilab Tevatron are fitted to obtain the non-perturbative long-distance matrix elements for different choices of unintegrated gluon distribution functions in the proton. Using the matrix elements thus obtained, we predict charmonium production rates in γγ, γp, and deepinelastic ep collisions including the contributions from both direct and resolved photons. The results are compared with the known ones obtained in the conventional parton model and with recent experimental data from HERA and LEP2.

The p T -spectra for direct J/ψ and ψ ′ in hadroproduction at Tevatron energy have been calculated within the framework of the NRQCD formalism and the fragmentation model in the collinear parton model as well as in the k T -factorization approach.We have described the CDF data and obtained a good agreement between the predictions of the parton model and the k T -factorization approach. We performed the calculations using the relevant leading order in α s hard amplitudes and taking equal values of the long-distance matrix elements for the both models. I. INTRODUCTIONDuring the years after the measuring of charmonium productiom cross sections and polarization effects for J/ψ and ψ ′ mesons at the Tevatron Collider [1] the phenomenology of a quarkonium production has a phase of intensive developments. Nowadays, it is understand that the heavy quarkonium production is a very complicated physical process needs many new theoretical ideas. Starting from the Color Singlet Model [2] it was developed, so-called, the nonrelativistic QCD (NRQCD) formalism [3] to describe the nonperturbative transition of QQ-pair into a final heavy quarkonium.The perturbative fragmentation functions for partons which split into heavy quarkonia have been obtained [4] within the framework of the NRQCD formalism. It is supposed that the fragmentation model is more adequate for the description of a quarkonium production at the large quarkonium transverse momentum p T ≫ M QQ than the fusion model. * Electronic address: saleev@ssu.samara.ru † Electronic address: vasin@ssu.samara.ru

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