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 P_gg splitting function for sufficiently small α_s, the minimum occurring formally at log(1/x)∼1/α_s. We calculate the properties of the dip, including corrections of relative order α_s, and discuss how this expansion in powers of α_s, which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of α_s. Finally, we note that the dip position, as a function of α_s, 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.