Sum rules for higher-twist parton distributions

TL;DR

This paper explores the theoretical connections between sum rules, dispersion relations, and delta-function contributions in higher-twist parton distributions, analyzing potential violations in experimental data.

Contribution

It provides a theoretical explanation for small violations of sum rules in twist-3 distributions and studies non-perturbative predictions using a one-loop model.

Findings

Sum rules may be violated at x≠0 due to delta-function contributions.

Dispersion relations relate sum rule violations to distribution function subtractions.

One-loop model predicts small deviations consistent with theoretical expectations.

Abstract

In deep-inelastic scattering experiments, there is a general connection between subtractions in dispersion relations, violations of sum-rules and $\delta$-functions in parton distribution functions. It is explained why one might expect a small violation in sum rules for the twist-3 distribution functions $g_T(x)$ and $h_L(x)$ when the sum-rules are applied to $x\neq 0$ data only. The non-perturbative predictions are studied in the context of a one-loop model.