Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators
P. A. Baikov, K. G. Chetyrkin, J. H. Kühn
TL;DR
This work generalizes the five-loop quark mass anomalous dimension gamma_m to arbitrary compact simple gauge groups by expressing the required renormalization constants through four-loop massless propagator integrals using infrared rearrangement and the R*-operation. The authors provide explicit formulas for the renormalization constants and gamma_m, recover known SU(3) and QED limits, and detail the transcendental structure with zeta values up to zeta(7). They also analyze the appearance and absence of even zetas in related observables, highlighting how five-loop corrections can introduce such constants in observables expressible via massless propagators. The results are validated against independent calculations (Luthe 2016) and have implications for precise Higgs decay predictions and the understanding of gauge-group dependence in high-order perturbation theory.
Abstract
We extend the ${\cal O}(α_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.