Double, triple, and $n$-parton scatterings in high-energy proton and nuclear collisions

TL;DR

This paper reviews the theoretical framework for calculating multi-parton scattering cross sections in high-energy proton and nuclear collisions, emphasizing the role of the effective cross section and providing numerical predictions for collider experiments.

Contribution

It introduces a unified approach to compute n-parton scattering cross sections using the effective cross section parameter and applies it to collider scenarios with detailed numerical estimates.

Findings

Cross sections for DPS and TPS can be derived from single-parton cross sections.

Numerical predictions for heavy-quark, quarkonia, and gauge boson production at LHC and FCC energies.

The effective cross section relates to the transverse parton profile via a Glauber model.

Abstract

The framework to compute the cross sections for the production of particles with high mass and/or large transverse momentum in double- (DPS), triple- (TPS), and in general $n$-parton scatterings, from the corresponding single-parton ($\sigma_{\rm SPS}$) values in high-energy proton-proton, proton-nucleus, and nucleus-nucleus is reviewed. The basic parameter of the factorized $n$-parton scattering ansatz is an effective cross section $\sigma_{\rm eff}$ encoding all unknowns about the underlying generalized $n$-parton distribution in the proton (nucleon). In its simplest and most economical form, the $\sigma_{\rm eff}$ parameter can be derived from the transverse parton profile of the colliding protons and/or nucleus, using a Glauber approach. Numerical examples for the cross sections and yields expected for the concurrent DPS or TPS production of heavy-quarks, quarkonia, and/or gauge bosons in proton and nuclear collisions at LHC and Future Circular Collider (FCC) energies are provided. The obtained cross sections are based on perturbative QCD predictions for $\sigma_{\rm SPS}$ at next-to-leading-order (NLO) or next-to-NLO (NNLO) accuracy including, when needed, nuclear modifications of the corresponding parton densities.