We discuss charm meson-meson pair production recently observed by the LHCb Collaboration at = 7 TeV in proton-proton scattering. We examine double-parton scattering (DPS) mechanisms of double production and following hadronization as well as double and mixed $g c\bar c gg \to D^{0}D^{0}gc \to D^{0}D^{0}$ hadronization calculated with the help of the scale-dependent KKKS08 fragmentation functions. A new single-parton scattering (SPS) mechanism of production is also taken into consideration. Calculated differential distributions as a function of transverse momentum of one of the mesons, pair invariant mass and azimuthal angle distributions are confronted with the measured ones. The manifestation of the new SPS mechanisms with fragmentation within the scale-dependent fragmentation scheme change the overall picture suitable for standard scale-independent fragmentation where only DPS mechanism is present. Some consequences of the new mechanisms are discussed

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