Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

Starting from the Fierz transform of the two-flavour 't Hooft interaction ( a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction ter ms augmented by an NJL type Lorentz scalar interaction responsible for dyna mical symmetry breaking and quark mass generation), we show that: (1) antis ymmetric tensor Nambu-Goldstone bosons appeal provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled tu this system acquire a non-ze ro mass. Axial-vector fields do not mix with antisymmetric tensor fields, s o there is no mass shift there.