Five-loop quark mass and field anomalous dimensions for a general gauge group

TL;DR

The authors extend the calculation of fundamental renormalization constants in QCD to general gauge groups at five loops in the MSbar scheme, focusing on the quark mass and quark field anomalous dimensions. Using a highly automated multi-loop framework with IBP reduction to master integrals and PSLQ-based analytic reconstruction, they derive analytic expressions for the five-loop coefficients in terms of general group invariants and zeta-values, and verify consistency with known SU(3) results and large-Nf expansions. The work delivers the first complete five-loop results for gamma_m in a general Lie group and provides the full gauge-parameter dependent five-loop result for gamma_2, offering a robust cross-check against established limits and enabling precise RG evolution of quark parameters beyond SU(3) QCD. These results pave the way for complete five-loop renormalization program by enabling reconstruction of Z_m, Z_2, and related constants for broader gauge theories.

Abstract

We present analytical five-loop results for the quark mass and quark field anomalous dimensions, for a general gauge group and in the MSbar scheme. We confirm the values known for the gauge group SU(3) from an independent calculation, and find full agreement with results available from large-Nf studies.

Figures (1)

• Figure 1: 5-loop master integrals with 12 lines that contribute to eqs. (\ref{['eq:lc0']})-(\ref{['eq:lc2']}). Each line denotes a massive propagator $1/(k^2+m^2)$, and each dot stands for an extra power of the corresponding propagator.