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Spontaneous Breaking of Chiral Symmetry as a Consequence of Confinement

A. N. Ivanov·N. I. Troitskaya·M. Faber·M. Schaler·M. Nagy
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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 $σ$ and takes the form at the leading order in the large-$N$ expansion $m=2 \sqrtσ/π$ with $σ=0.27$ 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.

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A. N. Ivanov, N. I. Troitskaya, M. Faber, M. Schaler, M. Nagy. 1993-06-11. Spontaneous Breaking of Chiral Symmetry as a Consequence of Confinement. https://arxiv.org/abs/hep-ph/9306243

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