An introduction to the perturbative QCD pomeron and to jet physics at large rapidities

TL;DR

This work surveys the perturbative QCD pomeron by deriving and solving the BFKL equation for gluon ladders exchanged in the t-channel and applying it to jet production at large rapidities. It connects high-energy resummation with observable Mueller-Navelet jets, showing how the singlet (pomeron) solution yields an energy-growing cross section and predicts decorrelation of jet kinematics as rapidity separation increases. The analysis highlights the role of multiregge kinematics, Lipatov vertices, and the need to include higher-order (NLL) corrections for accurate phenomenology, while acknowledging limitations from scale dependence and parton-density evolution. Overall, the framework provides a principled method to probe QCD dynamics in the semihard regime and to interpret jet phenomena at hadron colliders through the lens of the BFKL pomeron.

Abstract

In these lectures we discuss the Balitsky, Fadin, Kuraev, and Lipatov (BFKL) theory, which resums the leading logarithmic contributions to the radiative corrections to parton scattering in the high-energy limit, and we apply it to hadronic two-jet production at large rapidity intervals.

Figures (12)

• Figure 1: Plane of the jet rapidities. The solid curves are lines of constant ${\bar{y}}$, the dashed curves are lines of constant $y$.
• Figure 2: $g\, g \rightarrow g\, g$ scattering, with exchange of a gluon in the $\hat{t}$ channel. We label each external line with momentum, helicity and color.
• Figure 3: Two-jet production at the Tevatron and LHC colliders, as a function of the rapidity interval $y$, at $\bar{y} = 0$. The dashed and dot-dashed lines are respectively the exact and large-$y$ LO cross sections.
• Figure 4: $2\rightarrow 3$-gluons Feynman diagrams, with gluon $k_1$ emitted $a)$ from the gluon exchanged in the $\hat{t}$ channel; $b)$ in the initial-state bremsstrahlung from the upper line; $c)$ in the final-state bremsstrahlung from the upper line. We have neglected the helicity labels, and we have omitted the diagrams with bremsstrahlung emission from the lower line.
• Figure 5: One-loop corrections to the elastic amplitude $g g\rightarrow g g$, with $\hat{t}$-channel exchange of two gluons $a)$ in the $\hat{s}$-channel physical region and $b)$ in the $\hat{u}$-channel physical region.