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 similar or equal to 2000 in pPb as compared to those in proton-nucleon collisions at the same center-of-mass energy. Estimates for triple charm (c(c)over-bar) and bottom (b(b)over-bar) production in pPb collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order calculations for c(c)over-bar and b(b)over-bar single-parton cross sections. At root s(NN) = 8.8 TeV, about 10% of the pPb events have three a pairs produced in separate partonic interactions. At root s(NN) = 63 TeV, the pPb cross sections for triple-J/psi and triple-b(b)over-bar are O(1-10 mb). In the most energetic collisions of cosmic rays in the upper atmosphere, equivalent to root s(NN approximate to) 400 TeV, the TPS c(c)over-bar cross section equals the total p-Air inelastic cross section.