Direct $J/\psi$ hadroproduction in $k^-$ perpendicular factorization and the color octet mechanism

The hadroproduction of direct $J/\ensuremath{\psi}$ in the framework of the ${k}_{\ensuremath{\perp}}$-factorization approach is studied. The color-singlet contribution is essentially larger than in the collinear approach but is still an order of magnitude below the data. The deficit may be well described by the color octet contribution with the value of the matrix element $〈0|{O}_{8}^{J/\ensuremath{\psi}}{(}^{3}{S}_{1})|0〉$ substantially decreased in comparison with fits in the collinear factorization. This should lead to a reduction of the large transverse polarization, predicted in the collinear approach.