Chiral Nonsymmetric Interaction in Strong Coupled QCD

Abstract: Chiral symmetry in massless QCD is believed to be broken spontaneously. We discuss a possibility that the chiral symmetry is explicitly broken by QCD monopoles which appear only in strong coupled QCD. Namely, the monopole quark interaction explicitly breaks the chiral symmetry ( SU$_A(2)\times $U$_A$(1) ) just like bare quark mass terms. We show that the strength of the interaction is roughly $10$ times smaller than standard strong interactions. We describe it as an effective interaction $g'\bar{q}q\Phi^{\dagger}\Phi$ with the monopole field $\Phi$ and $g'$ being of the order of $(10\rm \,GeV)^{-1}$ or less. It produces small constituent quark masses less than $1$MeV when the monopoles condense ( $\langle\Phi\rangle\neq 0 $ ). We examine to what extent such a weak but explicit symmetry breaking interaction is allowed. In particular, examining Gell-Mann-Oakes-Renner relation we find that the presence of such a small symmetry breaking term is still allowed within the present accuracy of lattice gauge simulations. We predict some phenomenological effects caused by the chiral nonsymmetric monopole quark interaction. Quark confinement and chiral condensate ( $\langle\bar{q}q\rangle\neq 0$ ) arise simultaneously. The condensate $\langle\bar{q}q\rangle$ caused by the monopoles is proportional to monopole density and is estimated such that $(-\langle\bar{q}q\rangle)^{1/3}\sim 160$MeV. The weak monopole quark interaction leads to the small decay width of an observable monopole to hadrons.