Target mass corrections to electroweak structure functions and perturbative neutrino cross sections

We provide a complete and consistent framework to include subasymptotic perturbative as well as mass corrections to the leading twist $(\tau =2)$ evaluation of charged and neutral current weak structure functions and the perturbative neutrino cross sections. We reexamine previous calculations in a modern language and fill in the gaps that we find missing for a complete and ready-to-use “NLO $\xi$-scaling” formulary. In particular, as a new result we formulate the mixing of the partonic and hadronic structure function tensor basis in the operator approach to deep inelastic scattering. As an underlying framework we follow the operator product expansion in the manner of Georgi and Politzer that allows the inclusion of target mass corrections at arbitrary order in QCD and we provide explicit analytical and numerical results at NLO. We compare this approach with a simpler collinear parton model approach to $\xi$ scaling. Along with target mass corrections we include heavy quark mass effects as a calculable leading twist power suppressed correction. The complete corrections have been implemented into a Monte Carlo integration program to evaluate structure functions and/or integrated cross sections. As applications, we compare the operator approach with the collinear approximation numerically and we investigate the NLO and mass corrections to observables that are related to the extraction of the weak mixing angle from a Paschos-Wolfenstein-like relation in neutrino-iron scattering. We expect that the interpretation of neutrino scattering events in terms of oscillation physics and electroweak precision physics will benefit from our results.