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