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Double charm production in single- and double-parton scattering

We discuss production of two pairs of $c \bar c$ in proton-proton collisions at the LHC. Both double-parton scattering (DPS) and single-parton scattering (SPS) contributions are included in the analysis. Each step of DPS is calculated within $k_t$-factorization approach which effectively includes some next-to-leading order corrections. The discussed mechanisms unavoidably lead to the production of pairs of mesons: $D_i D_j$ (each containing $c$ quarks) or $\bar D_i \bar D_j$ (each containing $\bar c$ antiquarks). We calculate corresponding differential distribution for $(D^0 D^0$ + $\bar D^0 \bar D^0)$ production. Within large theoretical uncertainties the predicted DPS cross section is fairly similar to the cross section measured recently by the LHCb collaboration. We also 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 an off-shell matrix element squared calculated using recently developed techniques. The results are compared with our earlier result obtained within the collinear approach. Only slightly larger cross sections are obtained than in the case of the collinear approach but still the SPS mechanism contribution is much smaller than the DPS one. 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.