AGK Cutting Rules and Multiple Scattering in Hadronic Collisions

TL;DR

This work extends the AGK cutting rules to perturbative QCD by treating the Pomeron as a BFKL ladder and analyzing the couplings of n reggeized gluons to hadrons. By decomposing multi-gluon exchanges into symmetric and reggeizing components and enforcing vertex symmetries, the authors derive explicit AGK weightings and demonstrate cancellations of many multi-Pomeron corrections in inclusive jet observables, both in nonperturbative and pQCD contexts. The Mueller-Navelet jet example illustrates how hard color-singlet exchanges and ladder couplings shape single- and double-jet cross sections, revealing residual contributions that generate long-range rapidity correlations. The results provide theoretical constraints for modeling multi-parton interactions and saturation effects at high energies, highlighting the role of jet-vertex and inter-ladder dynamics rather than projectile-projectile exchanges alone.

Abstract

We discuss the AGK rules for the exchange of an arbitrary number of reggeized gluons in perturbative QCD in the high energy limit. Results include the cancellation of corrections to single jet and double jet inclusive cross sections, both for hard and soft rescattering contributions.

Figures (20)

• Figure 1: Graphical representation of a multi-Regge poles contribution to the elastic scattering amplitude. The zigzag lines represent pomerons.
• Figure 2: Representation of the $t$-channel content of the elastic amplitude: a) discontinuity across the $2$-poles cut in the $\omega$-plane, b) computation of the coupling $2\rightarrow$4 in the $t$-channel physical region and c) isolation of the Regge poles in the (12) and (34) channels. The crosses in a), b) indicate that the lines are on shell in angular momentum and $4$-momentum, resp.
• Figure 3: Some examples of the different $s$-channel cuts of the $2$-pomeron contribution: a) diffractive and b) multiperipheral intermidiate states.
• Figure 4: Exchange of four reggeized gluons in pQCD. The wavy lines represent reggeized gluons. The blobs above and below denote the functions ${\cal N}_4(\{\hbox{\boldmath $k$}_j\},\omega)$, computed in pQCD.
• Figure 5: Six point amplitude for the computation of the high-mass diffraction cross section in the triple Regge limit.