Quark condensate from confinement in QCD

TL;DR

This paper demonstrates that scalar confinement in QCD naturally leads to nonzero quark condensates, elucidating mechanisms for chiral symmetry breaking and providing expressions consistent with lattice data.

Contribution

It reveals how scalar confinement produces quark condensates and derives explicit formulas involving string tension and quark mass, aligning with lattice results.

Findings

Quark condensates are generated by scalar confinement.

Derived explicit formulas for condensates involving string tension.

Numerical results closely match lattice data.

Abstract

The scalar confinement in QCD is shown to produce the nonzero quark condensate for any current quark mass. Mechanisms for the Chiral Symmetry breaking and for the nonzero quark condensates are revealed. For the light and strange flavors the condensates are essentially chiral (proportional to (string tension)$^{3/2}$). The expressions for the quark condensates are obtained as a sum over non-chiral meson states, and, using the operator product expansion, as an explicit expression that involves the confining string tension and the current quark mass. The numerical results are fairly close to the lattice data.