Scale Invariance of gA/gV in Lorentz-Scalar and Lorentz-Vector Quark Confining Potentials

Abstract

We have systematically investigated a class of models which is characterised by Euler-Lagrange equations for the quark fields (Dirac equation) which contain bag-like (i.e. Lorentz-scalar) confining potentials and various Lorentz-vector (Coulomb-like and modified linear) confining potentials and report the results for gA/gV, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and ρ(r) (quark annihilation density). It is demonstrated that the effects of the Lorentz-vector potential on low-energy observables are naturally limited in the baryon sector by the "Klein paradox". A strong Lorentz-scalar confining potential can, however, tolerate a small admixture of a Lorentz-vector component. The one-gluon-exchange Lorentz-vector potential is characterized by two parameters αs and r0. The scale-invariance of gA/gV is manifest as a peculiar r0–independence. With Lorentz-vector potentials of the Coulomb form, gA/gV is independent of the quark mass. gA and the quark eigen-energy E0 (and hence also the nucleon mass) decrease considerably for increasing positive αs.