Quark Mass Anomalous Dimension to alpha_s**4

TL;DR

Analytically computes the quark mass anomalous dimension $\gamma_m$ to four-loop order in QCD, using four-loop p-integrals and the MS-bar scheme. The work relies on integration-by-parts, infrared rearrangement with the $R^*$-operation, and the MINCER program (with QGRAF-generated diagrams) to obtain $\gamma_0$–$\gamma_3$. It provides explicit expressions for these coefficients for SU($N$) with $n_f$ flavours and gives numerical QCD ($N=3$) and QED cases, including validation against prior results. It also discusses the four-loop beta-function and the running of heavy-quark masses, presenting running factors $c(x)$ for strange, charm, bottom and top thresholds and highlighting implications for high-precision mass determinations.

Abstract

We present the results of analytic calculation of the quark mass anomalous dimension to alpha_s**4.