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.

Low moments of the four-loop splitting functions in QCD

“…[7,8] is conceptually simpler, but the complexity of the computations scales very unfavourably with N. In the singlet sector, the latter is conceptually very involved, see refs. [9,10] and references therein, but computationally offers a range in N that is roughly twice as large as that for the route via DIS.…”

Renormalization of twist-two operators and four-loop splitting functions in QCD

“…With the methods presented above, in [28] we had determined the Feynman rules resulting from operator 𝑂 𝐴𝐵𝐶 to 𝑔 GV 𝑔 exhibit a complicated pattern, which involve transcendental functions: harmonic sums [61,62] as well as generalized harmonic sums [63], for example…”

“…In [28], we proposed a new method that enables the determination of GV counterterms with full-𝑛 dependence. We first explain the basic idea of the new method.…”