Dynamics Of Proton Spin : Role Of $qqq$ Force

TL;DR

This paper investigates the role of a direct three-quark ($qqq$) force in the proton's spin structure using a covariant light-front approach, revealing a new singularity linked to the $qqq$ force and estimating its contribution to the proton spin anomaly.

Contribution

It introduces a novel $qqq$ force modeled as a Mercedes-Benz type Y-shaped interaction within a covariant framework, connecting 3D and 4D Bethe-Salpeter equations for baryons.

Findings

Identifies a singularity in the 3D wave function due to the $qqq$ force.

Provides an estimate of the two-gluon contribution to the proton spin anomaly.

Demonstrates the impact of the $qqq$ force on baryonic transition amplitudes.

Abstract

The analytic structure of the $qqq$ wave function, obtained recently in the high momentum regime of QCD, is employed for the formulation of baryonic transition amplitudes via quark loops. A new aspect of this study is the role of a direct ($Y$-shaped, Mercedes-Benz type) $qqq$ force in generating the $qqq$ wave function. The dynamics is that of a Salpeter-like equation (3D support for the kernel) formulated covariantly on the light front, a la Markov-Yukawa Transversality Principle (MYTP) which warrants a 2-way interconnection between the 3D and 4D Bethe-Salpeter (BSE) forms for 2 as well as 3 fermion quarks. The dynamics of this 3-body force shows up through a characteristic singularity in the hypergeometric differential equation for the 3D wave function $\phi$, corresponding to a $negative$ eigenvalue of the spin operator $i \sigma_1.\sigma_2\times \sigma_3$ which is an integral part of the $qqq$ force. As a first application of this wave function to the problem of the proton spin anomaly, the two-gluon contribution to the anomaly yields an estimate of the right sign, although somewhat smaller in magnitude. Keywords: 3bodyforce; proton-spin; 2gluon anomaly; fractional correction $\theta$