Four-loop splitting functions at small x

A bstract We consider the expansion of small- x resummed DGLAP splitting functions at next-to-leading logarithmic (NLL) accuracy to four-loop order, namely next-to-next-to-next-to-leading order (N 3 LO). From this, we extract the exact LL and NLL small- x contributions to the yet unknown N 3 LO splitting functions, both in the standard MS̄ M S ¯ scheme and in the Q 0 MS̄ M S ¯ scheme usually considered in small- x literature. We show that the impact of unknown subleading logarithmic contributions (NNLL and beyond) at N 3 LO is significant, thus motivating future work towards their computation. Our results will be also needed in future to match NLL resummation to N 3 LO evolution. In turn, we propose an improved implementation of the small- x resummation and therefore release a new version of the resummation code (HELL 3.0) which contains these changes.