# Transcendental structure of multiloop massless correlators and anomalous dimensions

## TL;DR

This paper advances understanding of the $pi$-dependent terms in massless correlators and anomalous dimensions, extending calculations to 6- and 7-loop levels and confirming predictions with recent high-loop results.

## Contribution

It extends previous work by calculating higher-loop $pi$-dependent terms in massless correlators and RG functions, providing predictions that align with recent results.

## Key findings

- Predictions for 7-loop RG functions in $O(n)$ $phi^4$ theory match recent results.
- All 7- and 8-loop results for QCD and scalar theories agree with the predictions.
- Extended calculations to 6- and 7-loop correlators and RG functions.

## Abstract

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.