Triple parton scatterings in proton-nucleus collisions at high energies

A generic expression to compute triple-parton scattering (TPS) cross sections in high-energy proton–nucleus (pA) collisions is derived as a function of the corresponding single-parton cross sections and an effective parameter encoding the transverse parton profile of the proton. The TPS cross sections are enhanced by a factor of about $9\,A\simeq 2000$ in pPb as compared to those in proton–nucleon collisions at the same center-of-mass energy. Estimates for triple charm ( $\mathrm{c}\overline{\mathrm{c}}$ ) and bottom ( $\mathrm{b}\overline{\mathrm{b}}$ ) production in pPb collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order calculations for $\mathrm{c}\overline{\mathrm{c}}$ and $\mathrm{b}\overline{\mathrm{b}}$ single-parton cross sections. At $\sqrt{s_{_{\textsc {nn}}}}= 8.8$ TeV, about 10% of the pPb events have three $\mathrm{c}\overline{\mathrm{c}}$ pairs produced in separate partonic interactions. At $\sqrt{s_{_{\textsc {nn}}}}= 63$ TeV, the pPb cross sections for triple- $J/\psi $ and triple- $\mathrm{b}\overline{\mathrm{b}}$ are ${{\mathscr {O}}}$ (1–10 mb). In the most energetic collisions of cosmic rays in the upper atmosphere, equivalent to $\sqrt{s_{_{\textsc {nn}}}}\approx $ 400 TeV, the TPS $\mathrm{c}\overline{\mathrm{c}}$ cross section equals the total p–Air inelastic cross section.