Triple Parton Scatterings in High-Energy Proton-Proton Collisions

A generic expression to compute triple parton scattering cross sections in high-energy proton-proton (pp) collisions is presented as a function of the corresponding single parton cross sections and the transverse parton profile of the proton encoded in an effective parameter sigma(eff, TPS). The value of sigma(eff, TPS) is closely related to the similar effective cross section that characterizes double parton scatterings, and amounts to sigma(eff, TPS) = 12.5 +/- 4.5 mb. Estimates for triple charm (c (c) over bar) and bottom (b (b) over bar) production in pp collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order perturbative calculations for single c (c) over bar, b (b) over bar cross sections. At root s approximate to 100 TeV, about 15% of the pp collisions produce three c (c) over bar pairs from three different parton-parton scatterings.