Markov-Yukawa Transversality On Covariant Null-Plane: Baryon Form Factor And Magnetic Moments

Abstract

The baryon-$qqq$ vertex function governed by the Markov-Yukawa Transversality Principle ($MYTP$), is formulated via the Covariant Null-Plane Ansatz ($CNPA$) as a 3-body generalization of the corresponding $q{\bar q}$ problem, and employed to calculate the proton e.m. form factor and baryon octet magnetic moments.The e.m. coupling scheme is specified by letting the e.m. field interact by turn with the `spectator' while the two interacting quarks fold back into the baryon. The $S_3$ symmetry of the matrix element is preserved in all d.o.f.'s together. The $CNPA$ formulation ensures, as in the $q{\bar q}$ case, that the loop integral is free from the Lorentz mismatch disease of covariant instantaneity ($CIA$), while the simple trick of `Lorentz completion'ensures a Lorentz invariant structure. The $k^{-4}$ scaling behaviour at large $k^2$ is reproduced. And with the infrared structure of the gluonic propagator attuned to spectroscopy, the charge radius of the proton comes out at $0.96 fm$. The magnetic moments of the baryon octet, also in good accord with data, are expressible as $(a+bλ)/(2+λ)$, where $a,b$ are purely geometrical numbers and $λ$ a dynamics-dependent quantity. PACS: 11.10.St ; 12.90.+b ; 13.40.Fn Key Words : Baryon-$qqq$ Vertex; Markov-Yukawa Principle (MYTP); 3D-4D Interlinkage; Covariant null-plane (CNPA); e.m.form factor;baryon magneton.