Charmonium production at high energy in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math>-factorization approach

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 nonrelativistic quantum chromodynamics at leading order in the strong-coupling constant ${\ensuremath{\alpha}}_{s}$ and the relative velocity $v$. The transverse-momentum distributions of direct and prompt $J/\ensuremath{\psi}$-meson production measured at the Fermilab Tevatron are fitted to obtain the nonperturbative 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 $\ensuremath{\gamma}\ensuremath{\gamma}$, $\ensuremath{\gamma}p$, and deep-inelastic $ep$ 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.

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