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.