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 ${\sigma }_{\text{eff},\mathrm{TPS}}$. The value of ${\sigma }_{\text{eff},\mathrm{TPS}}$ is closely related to the similar effective cross section that characterizes double parton scatterings, and amounts to ${\sigma }_{\text{eff},\mathrm{TPS}}=12.5\pm 4.5\mathrm{mb}$. Estimates for triple charm ($c\overline{c}$) and bottom ($b\overline{b}$) production in $pp$ collisions at LHC and FCC energies are presented based on next-to-next-to-leading-order perturbative calculations for single $c\overline{c}$, $b\overline{b}$ cross sections. At $\sqrt{s}\approx 100\mathrm{TeV}$, about 15% of the $pp$ collisions produce three $c\overline{c}$ pairs from three different parton-parton scatterings.

Figure 1

Total charm (left) and bottom (right) cross sections in $pp$ collisions as a function of c.m. energy, in single parton (solid line) and triple parton (dashed line) scatterings. Bands around curves indicate scale, PDF (and ${\sigma }_{\text{eff},\mathrm{TPS}}$, in the case of ${\sigma }^{\mathrm{TPS}}$) uncertainties added in quadrature. The symbols are experimental data collected in Ref. [26].