The transverse momentum dependent statistical parton distributions revisited

TL;DR

This paper revisits the statistical parton distributions by incorporating transverse momentum dependence, considering the proton's finite longitudinal momentum, and analyzing implications for low $Q^2$ electron-proton collisions.

Contribution

It introduces a new approach to include TMD in statistical parton distributions considering finite proton momentum and Melosh-Wigner rotation effects.

Findings

TMD distributions generated via a transverse energy sum rule.

Relevance for low $Q^2$ electron-proton inelastic collisions.

Inclusion of Melosh-Wigner rotation effects on helicity distributions.

Abstract

The extension of the statistical parton distributions to include their transverse momentum dependence (TMD) is revisited by considering that the proton target has a finite longitudinal momentum. The TMD will be generated by means of a transverse energy sum rule. The new results are mainly relevant for electron-proton inelastic collisions in the low $Q^2$ region. We take into account the effects of the Melosh-Wigner rotation for the helicity distributions.