Can the triple-parton scattering be observed in open charm meson production at the LHC?

We investigate whether the triple-parton scattering effects can be observed in open charm production in proton-proton collisions at the LHC. We use so-called factorized Ansatz for calculations of hard multiple-parton interactions. The numerical results for each parton interaction are obtained within the kT-factorization approach. Predictions for one, two and three cc¯ pairs production are given for s=7 TeV and s=13 TeV. Quite large cross sections, of the order of milibarns, for the triple-parton scattering mechanism are obtained. We suggest a measurement of three D0 or three D0¯ mesons by the LHCb Collaboration. Confronting our results with recent LHCb experimental data for single and double D0 (or D0¯) meson production we present our predictions for triple meson final state: D0D0D0 or D0¯D0¯D0¯. We present cross sections for the LHCb fiducial volume as well as distributions for D0 meson transverse momentum and three-D0 meson invariant mass. The predicted visible cross sections, including the detector acceptance, hadronization effects and c→D0 branching fraction, is of the order of a few nanobarns. The counting rates including D0→K−π+ branching fractions are given for known or expected integrated luminosities.