Additional results on the four-loop flavour-singlet splitting functions in QCD

We have extended our previous computations, performed analytically for a general gauge group, of the even-N moments γik(3)(N) of the four-loop flavour-singlet splitting functions Pik(3)(x) to N=22. The numerical QCD results perfectly agree with all predictions resulting from the approximations for Pik(3)(x) that we obtained before from the moments N ≤ 20 and endpoint constraints, confirming their reliability for collider-physics applications. Due to the additional analytical constraints provided by our new N=22 results, we are now closing in on determining the all-N forms of all non-rational (ζ-function) contributions to γik(3)(N): only the nf0ζ3 parts of the quark-to-gluon (gq) and the nf1ζ3 parts of the gluon-to-gluon (gg) cases still need to be completed. Finally we extend our approximations for all Pik(3)(x) to nf=6 light flavours and update those for Pgq(3)(x) at lower nf.