Proton spin in leading order of the covariant approach

TL;DR

This paper investigates the covariant quark-parton model's impact on understanding proton spin, emphasizing relativistic effects on quark spins and orbital angular momentum, and compares it with the collinear approach.

Contribution

It introduces a Lorentz invariant 3D approach to calculate structure functions, accounting for angular momentum composition in a covariant framework.

Findings

Structure functions $g_{1}$ and $g_{2}$ satisfy experimental constraints.

Proton spin content $ extstylerac{1}{2}$ is consistent with $ extstylerac{1}{3}$ contribution from quarks.

The covariant approach aligns well with experimental data.

Abstract

We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $\Delta\Sigma\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.