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arXiv · 0712.2896

Dynamics Of Proton Spin : Role Of $qqq$ Force

A. N. Mitra
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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 $ϕ$, corresponding to a $negative$ eigenvalue of the spin operator $i σ_1.σ_2\times σ_3$ 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 $θ$

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A. N. Mitra. 2007-12-18. Dynamics Of Proton Spin : Role Of $qqq$ Force. https://arxiv.org/abs/0712.2896

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