Explicit calculation of the running coupling BFKL anomalous dimension

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. similar to x(-0.2) The NLO corrections to the anomalous dimension are rather small. unlike thr fixed coupling case, and a stable perturbative expansion is obtained. (C) 2000 Published by Elsevier Science B.V. All rights reserved.