Resummation of singlet parton evolution at small x

We propose an improvement of the splitting functions at small x which overc omes the apparent problems encountered by the BFKL approach. We obtain a st able expansion for the x-evolution function chi (M) near M = 0 by including in it a sequence of terms derived from the one- and two-loop anomalous dim ension gamma. The requirement of momentum conservation is always satisfied. The residual ambiguity on the splitting functions is effectively parameter ized in terms of the value of lambda, which fixes the small x asymptotic be haviour x(-lambda) of the singlet parton distributions. We derive from this improved evolution function an expansion of the splitting function which l eads to good apparent convergence, and to a description of scaling violatio ns valid both at large and small x. (C) 2000 Elsevier Science B.V. All righ ts reserved.