Spontaneous Breaking of Chiral Symmetry as a Consequence of Confinement

Abstract

We show that at the leading order in the large-$N$ expansion a lattice QCD motivated linear rising confinement potential at large distances leads to a non-local four-quark interaction that realizes spontaneous breaking of chiral symmetry (SBCS) in the same way the Nambu-Jona-Lasinio model does. The dynamical quark mass $m$, which represents the solution of the gap-equation, is proportional to the square root of the string tension $\sigma$ and takes the form at the leading order in the large-$N$ expansion $m=2\sqrt{\sigma }/\pi$ with $\sigma =0.27$ GeV${}^2$. The Nambu-Jona-Lasinio phenomenological constant $G_1$, which is responsible for SBCS, is expressed in terms of the string tension and the confinement radius.

Comments: 10 pages, 0 figures, latex, IK-TUW-Preprint 9305401