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 wavefunctions, while with the ``no pair'' variant of the Dirac equation only Lorentz vector confinement has normal Regge behaviour. A systematic investigation of Regge properties and phenomenological properties is carried out, including calculations of the Isgur-Wise 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 zero recoil point is found to be ${\xi }^{\prime }(1)\simeq -0.90$ for the Dirac equation with scalar confinement, and ${\xi }^{\prime }(1)\simeq -1.20$ for the no pair equation with vector confinement. Using heavy-light data alone we argue against scalar confinement.

Latex (uses epsf macro), 25 pages of text, 12 postscript figures included. One reference is added and some typos are fixed

References in corpus (3)

• Isgur-Wise Functions from the Mit Bag Model
• Relativistic Flux Tube Model Calculation of the Isgur-Wise Function
• Isgur - Wise Functions for Confined Light Quarks in a Colour Electric Potential

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• Chiral Symmetry Restoration using the Running Coupling Constant from the Light-Front Approach to QCD