Axial baryon number nonconserving antisymmetric tensor four-quark effective interaction

Abstract

We discuss the phenomenological consequences of the ${U}_{A}(1)$ symmetry-breaking two-flavor four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the ``duality'' symmetry of this interaction. Starting from the Fierz transform of the two-flavor 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by a Nambu--Jona-Lasinio- type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (1) Four antisymmetric tensor and four antisymmetric pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (2) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (3) The mixing of massive antisymmetric tensor fields with vector fields leads to two sets of spin-one states. The second set of spin-one mesons is heavy and has not been observed. Moreover at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the antisymmetric tensor interaction. The tachyonic state also shows up as a pole in the spacelike region of the EM form factors. (4) The axial-vector fields' mixing with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift of axial vector mesons is negligible. (5) The antisymmetric tensor version of the Veneziano-Witten ${U}_{A}(1)$ symmetry-breaking interaction does not lead to tachyons, or any antisymmetric tensor field propagation to leading order in ${N}_{C}.$