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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 σeff,TPS. The value of σeff,TPS is closely related to the similar effective cross section that characterizes double parton scatterings, and amounts to σeff,TPS=12.5±4.5 mb. Estimates for triple charm (cc̄) and bottom (bb̄) production in $pp$ collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order perturbative calculations for single cc̄, bb̄ cross sections. At √s≈100 TeV, about 15% of the $pp$ collisions produce three cc̄ pairs from three different parton-parton scatterings.
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d’Enterria et al. (2017) studied this question.
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