Quark Mass and Field Anomalous Dimensions to ${\cal O}(α_s^5)$

TL;DR

This work delivers the first complete analytic calculation of the quark mass and field anomalous dimensions at five loops in QCD, enabling precise renormalization-group running of quark masses and informing phenomenology such as Higgs decays to heavy quarks and Yukawa unification. The authors employ Infrared Rearrangement and the $R^*$-operation to reduce vast sets of five-loop propagator integrals to a small set of master integrals, yielding explicit $\gamma_m$ and $\gamma_2$ expressions with full $n_f$ and zeta-value dependence. They explore implications for the RG-improved (RGI) mass and Higgs decay rates, showing five-loop effects are currently small compared to existing uncertainties but could become relevant with future precision. The results underscore the need for the five-loop beta function to achieve a fully consistent five-loop running and point to ongoing work in that direction.

Abstract

We present the results of the first complete analytic calculation of the quark mass and field anomalous dimensions to ${\cal O}(α_s^5)$ in QCD.