Observations on the potential confinement of a light fermion

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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 ξ’(1)≃-0.90 for the Dirac equation with scalar confinement and ξ’(1)≃-1.20 for the no pair equation with vector confinement. Using heavy-light meson data alone we argue against scalar confinement.