Target Mass Corrections for Polarized Structure Functions and New Sum Rules

TL;DR

Target mass corrections for polarized deep inelastic scattering are computed for both neutral and charged currents using the Georgi–Politzer approach, yielding closed-form twist-2 and twist-3 corrections in Mellin moments and in $x$-space. The study shows that TMCs induce twist-3 contributions to all polarized structure functions, while preserving the Wandzura–Wilczek relation for twist-2 and introducing three new twist-3 relations, with additional mass-correction effects breaking Dicus/Callan-Gross-type relations. The results include explicit $x$-space representations with the Nachtmann variable and address threshold and resummation issues, highlighting implications for sum rules and low-$Q^2$ experiments. The Appendix confirms that quark-mass corrections do not violate WW, reinforcing the robustness of WW under mass effects.

Abstract

The target mass corrections are calculated for all structure functions of neutral and charged current deep inelastic scattering in lowest order in the coupling constant. Representations of the correction to the twist--2 and twist--3 contributions are derived both in Mellin-$n$ and $x$-space. The impact of the target mass corrections on the general relations between the twist--2 and twist--3 parts of the structure functions is studied and three new relations between the twist--3 contributions are derived.