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Production of two charm quark-antiquark pairs in single-parton scattering within the $k_t$-factorization approach

We present first results for the $2 \to 4$ single-parton scattering $g g \to c \bar c c \bar c$ subprocess for the first time fully within the $k_t$-factorization approach. In this calculation we have used the Kimber-Martin-Ryskin unintegrated gluon distribution which effectively includes some class of higher-order gluon emissions, and an off-shell matrix element squared calculated using recently developed techniques. The results are compared with our earlier result obtained within the collinear-factorization approach. Only slightly larger cross sections are obtained than in the case of the collinear approach. Inclusion of transverse momenta of gluons entering the hard process leads to a much stronger azimuthal decorrelation between $c c$ and $\bar c \bar c$ than in the collinear-factorization approach. A comparison to predictions of double parton scattering (DPS) results and the LHCb data strongly suggests that the assumption of two fully independent DPS ($g g \to c \bar c \otimes g g \to c \bar c$) may be too approximate.