Differences between charged-current coefficient functions

TL;DR

This paper provides detailed higher-order calculations of charged-current deep-inelastic scattering structure functions, including differences between crossing-even and -odd coefficient functions, with implications for sum rules and the Paschos-Wolfenstein ratio.

Contribution

It presents the first complete two- and three-loop results for these differences, including the longitudinal structure function and corrections to the Gottfried sum rule.

Findings

Confirmed suppression of differences at large number of colours

Computed lowest five moments at three loops for all structure functions

Derived small QCD contributions to the Paschos-Wolfenstein ratio

Abstract

Second- and third-order results are presented for the structure functions of charged-current deep-inelastic scattering in the framework of massless perturbative QCD. We write down the two-loop differences between the corresponding crossing-even and -odd coefficient functions, including those for the longitudinal structure function not covered in the literature so far. At three loops we compute the lowest five moments of these differences for all three structure functions and provide approximate expressions in Bjorken-$x$ space. Also calculated is the related third-order coefficient-function correction to the Gottfried sum rule. We confirm the conjectured suppression of these quantities if the number of colours is large. Finally we derive the second- and third-order QCD contributions to the Paschos-Wolfenstein ratio used for the determination of the weak mixing angle from neutrino-nucleon deep-inelastic scattering. These contributions are found to be small.