Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

TL;DR

This paper computes the four-loop anomalous dimension of non-singlet twist-two quark operators for arbitrary spin in SU(nc) gauge theory, providing exact functional forms of related splitting functions to improve theoretical precision.

Contribution

It presents the first closed-form expression for the zeta(3) part of the four-loop anomalous dimension for any Lorentz spin N in SU(nc) gauge theory, derived from Mellin moments.

Findings

Derived the zeta(3) term in the four-loop anomalous dimension for N=1,...,16.

Obtained exact x-space forms of splitting functions from Mellin moments.

Reduced uncertainties in splitting function approximations.

Abstract

Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory. Via Mellin transformation, we obtain the exact functional forms in x of the respective pieces of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting functions. This allows us to reduce the theoretical uncertainties in the approximations of these splitting functions otherwise amenable from the first few low-N values.