# Spin Dynamics Of $qqq$ Wave Function On Light Front In High Momentum Limit Of QCD : Role Of $qqq$ Force

## TL;DR

This paper investigates the influence of a spin-rich three-quark ($qqq$) force, generated by a gluon vertex, on the wave function of baryons in high-momentum QCD, revealing a singularity linked to spin effects and potential implications for the proton spin puzzle.

## Contribution

It introduces a novel spin-rich $qqq$ force derived from a $ggg$ vertex and analyzes its impact on the $qqq$ wave function using a covariant light-front approach.

## Key findings

- Identification of a singularity caused by the $qqq$ force's spin operator eigenvalue.
- Demonstration of the $qqq$ force's potential role in the proton spin anomaly.
- Formulation of a Salpeter-like equation incorporating $qq$ and $qqq$ forces.

## Abstract

The contribution of a spin-rich $qqq$ force (in conjunction with pairwise $qq$ forces) to the analytical structure of the $qqq$ wave function is worked out in the high momentum regime of QCD where the confining interaction may be ignored, so that the dominant effect is $Coulombic$. A distinctive feature of this study is that the spin-rich $qqq$ force is generated by a $ggg$ vertex (a genuine part of the QCD Lagrangian) wherein the 3 radiating gluon lines end on as many quark lines, giving rise to a (Mercedes-Benz type) $Y$-shaped diagram. 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. With these ingredients, the differential equation for the 3D wave function $\phi$ receives well-defined contributions from the $qq$ and $qqq$ forces. In particular a $negative$ eigenvalue of the spin operator $i \sigma_1.\sigma_2\times \sigma_3$ which is an integral part of the $qqq$ force, causes a characteristic singularity in the differential equation, signalling the dynamical effect of a spin-rich $qqq$ force not yet considered in the literature. The potentially crucial role of this interesting effect vis-a-vis the so-called `spin anomaly' of the proton, is a subject of considerable physical interest.