Renormalization of twist-two operators in covariant gauge to three loops in QCD

Abstract

The leading short-distance contributions to hadronic hard-scattering cross sections in the operator product expansion are described by twist-two quark and gluon operators. The anomalous dimensions of these operators determine the splitting functions that govern the scale evolution of parton distribution functions. In massless QCD, these anomalous dimensions can be determined through the calculation of off-shell operator matrix elements, typically performed in a covariant gauge, where the physical operators mix with gauge-variant operators of the same quantum numbers. We derive a new method to systematically extract the counterterm Feynman rules resulting from these gauge-variant operators. As a first application of the new method, we rederive the unpolarized three-loop singlet anomalous dimensions, independently confirming previous results obtained with other methods. Employing a general covariant gauge, we observe the explicit cancellation of the gauge parameter dependence in these results.

4 figures, 1 table, extends previous results in proceedings arXiv:2207.10108, ancillary files with results

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Cited by in corpus (3)

• FeynCalc 10: Do multiloop integrals dream of computer codes?
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$