Transverse Force on Transversely Polarized Quarks in Longitudinally Polarized Nucleons

TL;DR

This paper explores the semi-classical interpretation of certain moments of twist-3 PDFs, linking the $x^3$ moment of $h_L^3(x)$ to the transverse force on transversely polarized quarks in longitudinally polarized nucleons, with implications for nucleon spin decompositions.

Contribution

It establishes a relation between the $x^3$ moment of $h_L^3(x)$ and the transverse force on polarized quarks, providing new insights into nucleon spin structure and force interpretations.

Findings

The $x^3$ moment of $h_L^3(x)$ relates to the transverse force on polarized quarks.

No semi-classical interpretation found for higher moments of $g_T(x)$ and $e(x)$.

Implications for the Jaffe-Manohar and Ji nucleon spin decompositions.

Abstract

We study the semi-classical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semi-classical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was find, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a DIS experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between tha Jaffe-Manohar and the Ji decompositions of the nucleon spin.