Unified model of the Nambu-Jona-Lasinio type for all elementary-particle forces

Abstract

The unified model for all elementary-particle forces recently proposed by us is discussed in detail. Starting with a nonlinear fermion Lagrangian of the Nambu-Jona-Lasinio type and imposing the massless conditions of Bjorken on vector fields, we construct an effective Lagrangian which combines the unified guage theory of Weinberg and Salam for the weak and electromagnetic interactions of leptons and quarks and the asymptotically free gauge theory of Gross, Wilczek, and Politzer for the strong interaction of quarks. The photon, weak vector bosons, and Higgs scalars appear as composites of lepton-antilepton or quark-antiquark pairs, while the color-octer gluons appear as composites of quark-antiquark pairs. As a result, the Weinberg angle is determined to be ${sin}^{2}{\ensuremath{\theta}}_{W} = \frac{3}{8}$ for fractionally charged quarks, which coincides with the prediction of Georgi and Glashow in their unified SU(5) gauge model. The gluon coupling constant is also determined to be 8/3 times the fine-structure constant. The masses of the weak vector bosons and physical Higgs scalars are related to those of leptons and quarks. We also propose a unified spinor-subquark model in which the gauge bosons and Higgs scalars as well as leptons and quarks are all composites of subquarks of spin 1/2. In such a model, we predict, among other things, the mass of the charged weak vector bosons to be approximately $\sqrt{3}$ times the subquark mass. From these results, we strongly suggest that there exist much heavier leptons and/or quarks whose masses reach or go beyond the weak-vector-boson masses or that there exist heavy subquarks whose pair-production threshold lies very close to the weak-vector-boson masses.