Scale invariance of (gA)/(gV) in Lorentz-scalar and Lorentz-vector quark confining potentials

摘要

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 g(A)/g(V), mu(p)(quark), [r(q)(2)](1/2), (r(pi)(NN)(2))(1/2), E-0(quark) and rho(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 alpha(s) and r(0). The scale-invariance of g(A)/g(V) is manifest as a peculiar r(0)-independence. With Lorentz-vector potentials of the Coulomb form, g(A)/g(V) is independent of the quark mass. ga and the quark eigen-energy E-0 (and hence also the nucleon mass) decrease considerably for increasing positive alpha(s). [References: 43]