Dynamical Quark Mass Generation Research Articles

QUARK CONFINEMENT AND DYNAMICAL CHIRAL SYMMETRY BREAKDOWN IN QCD

In the framework of the Schwinger-Dyson equation and corresponding Slavnov-Taylor identity in the infrared region, we obtain nonperturbative, infrared finite and gauge-invariant quark propagator, which has no pole (confinement-type solution) and implies dynamical chiral symmetry breakdown (dynamical quark mass generation). Our model is free of ghost complications. Nonperturbative (effective) quark mass is derived, which exhibits an essential singularity in the coupling constant, according to the renormalization group solutions in the infrared region.

Quark masses and their hierarchies

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Quarksq (and leptonsl) are assumed to be produced by hypercolor confinement of preons at an intermediate scaleΛ hc. Hierarchies observed in theq mass spectra can be explained by a BCS mechanism if the color interaction is enough asymptotically free and if residual ones emerging by the confinement are medium strong. The former assumption claims thatN≦4, whereN is the family number ofq andl. Dynamical equations to determineq masses and mixings are given, but they require knowledge on the physics atΛ hc. A phenomenological approach is also made on the basis of anSU(7)×SU(7) chiral preon model withN=4. The mass ratiom t/mb is related to (m c/m s)ηB withη B≃1.1 andm t'/mb' to (m u/m d)ηA withη A≃1.4. In this scheme the fourth down quark is the heaviest (∼ 110 GeV) and contributes dominantly toF 2, whereF is the Fermi scale.

Quantum-field theory and the dynamical generation of quark masses

The dynamical generation of quark masses is discussed in terms of quark–antiquark, gluon–gluon, and quark–antiquark– gluon condensates. The quark–antiquark condensate is shown to contribute in a gauge-invariant manner to the dynamical quark mass. Arguments are put forward to suggest that the other condensates contribute only to the wave-function renormalization of the quark field and not to the magnitude of the dynamical quark mass.

Electroweak symmetry breaking with hierarchical feature

Electroweak symmetry breaking is attributed to dynamical generation of quark masses. Our study is made in those models in which preons are confined by hypercolor gauge interactions to form massless quarks and leptons as well as heavy hyperhadrons or postons. The hierarchical nature of the breaking can be understood by assuming the necessity of infinite-range color interactions in addition to short-range postonic ones. Self-consistent mass equations forN families of quarks are given in an ideal limit in which left-right asymmetric effects and quark-lepton couplings are neglected.

The Vacuum Structure of Quantum Chromodynamics

The vacuum structure of quantum chromodynamics (QCD) is studied, with emphasis on massless QCD. An interacting gas of instantons is replaced by an ideal gas of effective instantons, which incorporate effects of new tunnelings. The existence of a critical value θc in the θ-vacua is shown. Chirally asymmetric vacua of massless QCD require two-parameter dependence, which allows dynamical quark mass generation. Chiral U(N)⊗U(N) symmetry is realized in the Goldstone mode at |θ| = θc. The U(1) Goldstone boson becomes massive for θ, |θ|≪θc.