The structure of generic anomalous dimensions and no-$\pi$ theorem for massless propagators

Understand

Extending an argument of [Baikov:2010hf] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic \MSbar\ anomalous dimensions as well as in generic massless correlators.

• In particular, we find a new remarkable connection between coefficients in front of $\zeta_3$ and $\zeta_4$ in the 4-loop and 5-loop contributions to the QCD $\beta$-function respectively.
• It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the $\pi$-dependent terms in one-scale Renormalization Group (RG) invariant Euclidian quantities recently discovered in \cite{Jamin:2017mul}.
• We give a proof of this no-$\pi$ theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators.