Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension
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.
Cite
@article{arxiv.hep-ph/9912284,
title = {Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension},
author = {R. S. Thorne},
journal= {arXiv preprint arXiv:hep-ph/9912284},
year = {2009}
}
Comments
Tex file, including a modification of Harvmac, 15 pages, 5 figures as .ps files