Spin dynamics of qqq wave function on light front in high momentum limit of QCD: Role of qqq force

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 ϕ receives well-defined contributions from the qq and qqq forces. In particular a negative eigenvalue of the spin operator iσ1·σ2×σ3 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.