Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension

TL;DR

This paper derives an exact analytic expression for the gluon anomalous dimension from the running coupling BFKL equation, revealing a weaker small-x behavior and stable NLO corrections, improving understanding of Q^2 evolution.

Contribution

It provides a precise analytic calculation of the gluon anomalous dimension from the running coupling BFKL equation, highlighting differences from fixed coupling results.

Findings

An exact analytic form of the anomalous dimension is obtained.

The small-x splitting function behaves as x^(-0.2), indicating weaker divergence.

NLO corrections are small, leading to a stable perturbative expansion.

Abstract

I calculate the anomalous dimension governing the Q^2 evolution of the gluon (and structure functions) coming from the running coupling BFKL equation. This may be expressed in an exact analytic form, up to a small ultraviolet renormalon contribution, and hence the corresponding splitting function may be determined precisely. Rather surprisingly it is most efficient to expand the gluon distribution in powers of alpha_s(Q^2) rather than use the traditional expansion where all orders of alpha_s\ln(1/x) are kept on an equal footing. The anomalous dimension is very different from that obtained from the fixed coupling equation, and leads to a powerlike behaviour for the splitting function as x ->0 which is far weaker, i.e. about x^(-0.2). The NLO corrections to the anomalous dimension are rather small, unlike the fixed coupling case, and a stable perturbative expansion is obtained.