Some time ago two of us predicted that at large energies relevant for the LHC the production of double charm should be dominated by the double-parton scattering (DPS) mechanism [1]. Those studies of double $c \bar c$ production was extended next to the $k_t$-factorization approach which includes effectively higher-order QCD effects [2,3]. A relatively good description of the LHCb experimental data [4] was achieved for both the total yield and the dimeson correlation observables. The single-parton scattering (SPS) $g g \to c \bar c c \bar c$ contribution was discussed carefully in both collinear [3] and $k_t$-factorization [5] approaches. Their contribution to the $c \bar c c \bar c$ cross section was found to be rather small and was not able to describe details of the LHCb data.
Here we discuss production of $D^0 D^0$ (and ${\bar D}^0 {\bar D}^0$) pairs within an alternative approach where $g \to D$ fragmentation is included [6]. We consider double-parton scattering (DPS) mechanisms of double $c \bar c$ production and subsequent $cc \to D^{0}D^{0}$ hadronization as well as double $g$ and mixed $g c\bar c $ production with $gg \to D^{0}D^{0}$ and $gc \to D^{0}D^{0}$ hadronization calculated with the help of the scale dependent hadronization functions of Kniehl et al. Single-parton scattering (SPS) mechanism of digluon production is also taken into account. We compare our results with several correlation observables in azimuthal angle $\varphi_{D^{0}D^{0}}$ between $D^{0}$ mesons or in dimeson invariant mass $M_{D^{0}D^{0}}$. The inclusion of new mechanisms with $g \to D^{0}$ fragmentation leads to larger cross sections, than when including only DPS mechanism with standard scale independent $cc \to D^{0}D^{0}$ fragmentation functions. Some consequences of the presence of the new mechanisms are discussed. In particular a larger $\sigma_{eff}$ is needed to describe the LHCb data. There is a signature that $\sigma_{eff}$ may depend on transverse momentum of $c$ quarks and/or $\bar c$ antiquarks.
[1] M. Luszczak, R. Maciula and A. Szczurek, Production of two $c \bar c$ pairs in double-parton scattering,
Phys. Rev. D 85, 094034 (2012).
[2] R. Maciula and A. Szczurek, Production of $c \bar c c \bar c$ in double-parton scattering within $k_{t}$-factorization approach - meson-meson correlations, Phys. Rev. D 87, 074039 (2013).
[3] A. van Hameren, R. Maciula and A. Szczurek, Single-parton scattering versus double-parton scattering in the production of two $c \bar c$ pairs and charmed meson correlations at the LHC, Phys. Rev. D 89, 094019 (2014).
[4] R. Aaij et al. [LHCb Collaboration], Observation of double charm production involving open charm in pp collisions at $\sqrt{s}$ = 7 TeV, J. High Energy Phys. 06, 141 (2012); [J. High Energy Phys. 03, 108 (2014)].
[5] A. van Hameren, R. Maciula and A. Szczurek, Production of two charm quark-antiquark pairs in single-parton scattering within the $k_t$-factorization approach, Phys. Lett. B 748, 167 (2015).
[6] R. Maciula and V. A. Saleev, A. V. Shipilova and A. Szczurek, arXiv:1601.06981 [hep-ph].