In this paper we study the breaking of chiral symmetry with nonconfining powerlike potentials. The region of allowed exponents is identified and, after the previous study of confining (positive exponent) potentials, we now specialize in shorter range nonconfining potentials, with a negative exponent. These nonconfining potentials are close to the Coulomb potential, and they are also relevant as corrections to the linear confinement, and as models for the quark potential at the deconfinement transition. The mass-gap equation is constructed and solved, and the quark mass, the chiral angle, and the quark energy are calculated analytically with an exponent expansion in the neighborhood of the Coulomb potential. It is demonstrated that chiral symmetry breaking occurs, but only the chiral invariant false vacuum and a second nontrivial vacuum exist. Moreover chiral symmetry breaking is led by the ultraviolet part of the potential, with no infrared enhancement of the quark mass. Thus the breaking of chiral symmetry driven by nonconfining potentials differs from the one lead by confining potentials.

• Received 3 November 2008

DOI:https://doi.org/10.1103/PhysRevD.79.094030