Speaker
Description
We have computed the even-N moments of splitting functions at four-loop order in perturbative QCD, using off-shell operator renormalization for a general gauge group. These results agree with previous data and, combined with endpoint constraints, allowed us to develop precise approximations for the four-loop splitting functions, reducing uncertainties to about 1\% for relevant collider energies. Additionally, we addressed the mixing of gauge-invariant with gauge-variant operators using generalized BRST symmetry, an essential step for four-loop operator renormalization. A key innovation is our method for reconstructing all-N analytic expressions by solving systems of Diophantine equations, guided by conformal symmetry and reciprocity properties. This approach enables the derivation of high-order splitting functions from finite moments efficiently and systematically, advancing the theoretical precision of QCD evolution predictions for collider physics.