Small-x physics in perturbative QCD

TL;DR

The article develops a cohesive, field-theoretic treatment of small-$x$ QCD by connecting the parton-model picture with Regge theory through the BFKL pomeron, which is realized as a two-reggeized-gluon bound state. It introduces a gauge-invariant effective action for reggeized gluons, derives reggeon vertices, and analyzes both leading and next-to-leading contributions, including the structure of infrared divergences and their cancellations. The BKP framework for multi-reggeon states and the Möbius-conformal properties of the BFKL dynamics provide deep insights into the high-energy limit and unitarization strategies. The work also outlines the ongoing program to incorporate higher-order corrections and non-perturbative effects, with implications for small-$x$ structure functions and diffractive processes in deep inelastic scattering. Overall, it lays a formal foundation for perturbative small-$x$ QCD and points toward avenues for refining predictions and achieving a unitary high-energy theory.

Abstract

We review the parton model and the Regge approach to the QCD description of the deep-inelastic $ep$ scattering at the small Bjorken variable $x$ and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schrödinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed.