k-Factorization and Small-x Anomalous Dimensions

TL;DR

The article develops a two-scale NL BFKL framework in the Q0-scheme to reconcile high-energy k-factorization with RG evolution in small-x QCD, including running coupling effects and NL anomalous dimensions. It provides resummation formulas for coefficient functions and anomalous dimensions, and computes the NL q qbar contributions to the gluon channel, introducing a two-eigenvalue anomalous-dimension structure (gamma_plus and gamma_minus) that governs the evolution. The work identifies the regime where RG consistency holds (t ≫ t0 with controlled α_s(t) log(1/x)) and shows that running coupling induces notable but structured NL corrections, mainly in the qbarq sector, while higher-order NL effects are relatively small for the leading eigenvalue. It also emphasizes the diffusion into the IR as a source of Pomeron sensitivity and outlines the need for a complete gluonic NL kernel to fully exploit the framework for phenomenology.

Abstract

We investigate the consistency requirements of the next-to leading BFKL equation with the renormalization group, with particular emphasis on running coupling effects and NL anomalous dimensions. We show that, despite some model dependence of the bare hard Pomeron, such consistency holds at leading twist level, provided the effective variable $α_s(t) log(1/x)$ is not too large. We give a unified view of resummation formulas for coefficient functions and anomalous dimensions in the Q_0-scheme and we discuss in detail the new one for the $q\bar{q}$ contributions to the gluon channel.

Figures (6)

• Figure 1: BFKL equation for the gluon density up to next-to-leading level. Wavy lines denote (Regge) gluon exchanges.
• Figure 3: (a) $q\bar{q}$ and (b) low energy $gg$ contributions to the NL kernel, together with (c) one-loop corrections to $1g$ state and (d) two-loop virtual corrections.
• Figure 4: $q\bar{q}$ contribution to the 4 (Regge) gluon amplitude absorptive part.
• Figure 5: $q\bar{q}$ contributions to the BFKL eigenvalue as function of the anomalous dimension variable $\gamma$.
• Figure 6: $q\bar{q}$ contribution to the largest eigenvalue of the anomalous dimension matrix $\gamma_+$.