  We give a short account of recent advances in our understanding of the
$\pi$-dependent terms in massless (Euclidean) 2-point functions as well as in
generic anomalous dimensions (ADs) and $\beta$-functions. We extend the
considerations of \cite{Baikov:2018wgs} by two more loops, that is for the case
of 6- and 7-loop correlators and 7- and 8-loop renormalization group (RG)
functions. Our predictions for the ($\pi$-dependent terms) of the 7-loop RG
functions for the case of the $O(n)$ $\phi^4$ theory are in full agreement with
the recent results from \cite{Schnetz:2016fhy}. All available 7- and 8-loop
results for QCD and the scalar $O(n)$ $\varphi^4$ theory obtained within the
large $N_f$ approach to the quantum field theory (see, e.g.
\cite{Gracey:2018ame}) are also in full agreement with our results.
