The gluon splitting function at moderately small x

It is widely believed that at small x, the BFKL resummed gluon splitting function should grow as a power of 1/x. But in several recent calculations it has been found to decrease for moderately small-x before eventually rising. We show that this 'dip' structure is a rigorous feature of the 1, splitting function for sufficiently small alpha(s), the miminum occurring formally at log(1/x) similar to 1/ rootalpha(s). We calculate the properties of the dip, including corrections of relative order rootalpha(s), and discuss how this expansion in powers of which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of alphas, Finally, we note that the dip position, as a function of a, provides a lower bound in x below which the NNLO fixed-order expansion of the splitting function breaks down and the resummation of small-x terms is mandatory. (C) 2004 Published by Elsevier B.V.