New results on small-x resummation for splitting functions

A

bstract

We revisit the basic steps necessary to obtain next-to-leading-logarithmic accurate small- x results for the DGLAP splitting functions, and their implementations within the HELL framework. We derive new analytical all-order results for the leading-logarithmic gg anomalous dimension, the qg and gg finite Green functions, and most importantly for the qg anomalous dimension, which allows us to arrive for the first time at a properly resummed qg splitting kernel. We use these results as cornerstones of a new implementation of small- x splitting-function resummation which is more solid and numerically better behaved with respect to those available thus far. All of these novelties are included in the upcoming 4.0 version of HELL.