In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of J/psi mesons associated with open-charm particles at HERA and Tevatron conditions. We show that the contribution from J/psi+c+(c) over bar channel becomes comparable with that of J/psi sole production at high J/psi transverse momenta (approximately, at p(psi,T)> 10 GeV). We investigate the J/psi polarization effects and kinematic correlations between J/psi mesons and the accompanying open-charmed mesons. We show that the correlations are sensitive to the initial k(t) of the colliding partons, and so, can be considered as an additional test discriminating the collinear parton model and the k(t)-factorization approach.
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