Triple-parton scatterings in proton–nucleus collisions at high energies

Abstract

Abstract 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 $$9\,A\simeq 2000$$ 9A≃2000 in pPb as compared to those in proton–nucleon collisions at the same center-of-mass energy. Estimates for triple charm ($$\mathrm{c}\overline{\mathrm{c}}$$ cc¯ ) and bottom ($$\mathrm{b}\overline{\mathrm{b}}$$ bb¯ ) production in pPb collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order calculations for $$\mathrm{c}\overline{\mathrm{c}}$$ cc¯ and $$\mathrm{b}\overline{\mathrm{b}}$$ bb¯ single-parton cross sections. At $$\sqrt{s_{_{\textsc {nn}}}}= 8.8$$ sNN=8.8 TeV, about 10% of the pPb events have three $$\mathrm{c}\overline{\mathrm{c}}$$ cc¯ pairs produced in separate partonic interactions. At $$\sqrt{s_{_{\textsc {nn}}}}= 63$$ sNN=63 TeV, the pPb cross sections for triple-$$J/\psi $$ J/ψ and triple-$$\mathrm{b}\overline{\mathrm{b}}$$ bb¯ are $${{\mathscr {O}}}$$ O (1–10 mb). In the most energetic collisions of cosmic rays in the upper atmosphere, equivalent to $$\sqrt{s_{_{\textsc {nn}}}}\approx $$ sNN≈ 400 TeV, the TPS $$\mathrm{c}\overline{\mathrm{c}}$$ cc¯ cross section equals the total p–Air inelastic cross section.