Explicit calculation of the running coupling BFKL anomalous dimension

I calculate the anomalous dimension governing the Q(2) evolution of the glu on (and structure functions) coming from the running coupling BFKL equation . This may be expressed in an exact analytic form, up to a small ultraviole t renormalon contribution, and hence the corresponding splitting function m ay be determined precisely. Rather surprisingly it is most efficient to exp and 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 eq ual footing. The anomalous dimension is very different from that obtained f rom 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 th r fixed coupling case, and a stable perturbative expansion is obtained. (C) 2000 Published by Elsevier Science B.V. All rights reserved.