On the importance of Lorentz structure in the parton model: target mass corrections, transverse momentum dependence, positivity bounds

TL;DR

This paper emphasizes the critical role of Lorentz covariance in the parton model, showing it resolves discrepancies in polarized structure functions, derives target-mass and transverse momentum corrections, and improves bounds on parton densities.

Contribution

It demonstrates the importance of Lorentz structure in deriving accurate polarized structure functions, target-mass corrections, and bounds on parton densities without relying on operator expansion.

Findings

Correct Lorentz covariance resolves contradictions in g_2(x) results.

Derived target-mass corrections for polarized deep inelastic scattering.

Established stronger positivity and Soffer bounds for parton densities.

Abstract

We show that respecting the underlying Lorentz structure in the parton model has very strong consequences. Failure to insist on the correct Lorentz covariance is responsible for the existence of contradictory results in the literature for the polarized structure function g_2(x), whereas with the correct imposition we are able to derive the Wandzura-Wilczek relation for g_2(x) and the target-mass corrections for polarized deep inelastic scattering without recourse to the operator product expansion. We comment briefly on the problem of threshold behaviour in the presence of target-mass corrections. Careful attention to the Lorentz structure has also profound implications for the structure of the transverse momentum dependent parton densities often used in parton model treatments of hadron production, allowing the k_T dependence to be derived explicitly. It also leads to stronger positivity and Soffer-type bounds than usually utilized for the collinear densities.