Transcendental structure of multiloop massless correlators and anomalous dimensions

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 $O(n)$ ${\varphi }^4$ 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 $O(n)$ ${\phi }^4$ 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.

few typos corrected, the version accepted for publication

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Cited by in corpus (8)

• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Glue-and-Cut at Five Loops
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• Higher-order behaviour of two-point current correlators
• Correlators of vector, tensor, and scalar composite vertices of order $O({\alpha }_s^2{\beta }_0)$
• Landau-Khalatnikov-Fradkin transformation and hatted zeta-values