Observations on the potential confinement of a light fermion

Abstract

We consider possible dynamical models for a light fermion confined by a potential field. With the Dirac equation only Lorentz scalar confinement yields normalizable wave functions, while with the ``no pair'' variant of the Dirac equation only Lorentz vector confinement has normal Regge behavior. A systematic investigation of Regge properties and phenomenological properties is carried out, including calculations of the Isgur-Wise (IW) function. We point out that the Isgur-Wise function provides a sensitive test of confinement models. In particular, the slope of the IW function at the zero recoil point is found to be \ensuremath{\xi}'(1)\ensuremath{\simeq}-0.90 for the Dirac equation with scalar confinement and \ensuremath{\xi}'(1)\ensuremath{\simeq}-1.20 for the no pair equation with vector confinement. Using heavy-light meson data alone we argue against scalar confinement.