Hard scattering cross sections at LHC in the Glauber approach: from pp to pA and AA collisions

TL;DR

The paper formulates hard-scattering observables in pA and AB collisions at LHC energies within the Glauber geometric framework, deriving inelastic and hard-process cross-sections from NN cross-sections and nuclear thickness/overlap functions. It provides compact expressions for MB cross-sections and yields, and clarifies how yields scale with geometry via ⟨T_A⟩ and ⟨T_AB⟩, as well as the binary-collision baseline ⟨N_coll⟩. The approach yields practical formulas for centrality-dependent yields and cross-sections, enabling interpretation of high-pT probes in pA and AA collisions. Numerical examples for p+Pb at 8.8 TeV and Pb+Pb at 5.5 TeV illustrate the expected MB scaling and overlap functions, informing LHC phenomenology.

Abstract

The scaling rules of the invariant yields and cross sections for hard scattering processes in proton-nucleus ($pA$) and nucleus-nucleus ($AB$) reactions at LHC energies relative to those of nucleon-nucleon $NN$ (isospin averaged $pp$) collisions are reviewed within the Glauber geometrical formalism. The number of binary inelastic collisions for different centrality classes in p+Pb and Pb+Pb collisions at $\sqrt{s_{NN}}$ = 8.8 TeV and 5.5 TeV respectively, as obtained from a Glauber Monte Carlo, are also given.