NNLO evolution of deep-inelastic structure functions: the non-singlet case

TL;DR

This paper analyzes the NNLO evolution of non-singlet structure functions in QCD, providing parametrizations, assessing uncertainties, and demonstrating reduced theoretical errors in alpha_s determinations.

Contribution

It offers new NNLO parametrizations of non-singlet quark densities and structure functions, including uncertainty estimates and compact expressions for two-loop coefficient functions.

Findings

NNLO corrections improve stability under scale variations

Residual uncertainties are negligible for x > 10^-2

Inclusion of NNLO reduces alpha_s uncertainty by over a factor of two

Abstract

We study the next-to-next-to-leading order (NNLO) evolution of flavour non-singlet quark densities and structure functions in massless perturbative QCD. Present information on the corresponding three-loop splitting functions is used to derive parametrizations of these quantities, including Bjorken-x dependent estimates of their residual uncertainties. Compact expressions are also provided for the exactly known, but rather involved two-loop coefficient functions. The size of the NNLO corrections and their effect on the stability under variations of the renormalization scale are investigated. The residual uncertainty of the three-loop splitting functions does not lead to appreciable effects for x > 10^-2. Inclusion of the NNLO contributions reduces the main theoretical uncertainty of alpha_s determinations from non-singlet scaling violations by more than a factor of two.