Abstract
Extending an argument of [1] 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 \( \overline{\mathrm{MS}} \) anomalous dimensions as well as in generic massless correlators. In particular, we find a new remarkable connection between coefficients in front of ζ3 and ζ4 in the 4-loop and 5-loop contributions to the QCD β-function respectively. It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the π-dependent terms in one-scale Renormalization Group (RG) invariant Euclidean quantities recently discovered in [2]. We give a proof of this no-π theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators. All π-dependent terms in the six-loop coefficient of an anomalous dimension (or a β-function) are shown to be explicitly expressible in terms of lower order coefficients for a general one-charge theory. For the case of a scalar O(n) ϕ4 theory all our predictions for π-dependent terms in 6-loop anomalous dimensions are in full agreement with recent results of [3,4,5].
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Baikov, P.A., Chetyrkin, K.G. The structure of generic anomalous dimensions and no-π theorem for massless propagators. J. High Energ. Phys. 2018, 141 (2018). https://doi.org/10.1007/JHEP06(2018)141
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DOI: https://doi.org/10.1007/JHEP06(2018)141