Compositeantisymmetric tensor bosons in a four-fermion interactionmodel

Abstract

We discuss the phenomenological consequences of the UA(1) symmetry-breaking two-flavour four-fermionantisymmetric (AS) Lorentz tensor interaction Lagrangians. Weuse the recently developed methods that respect the `duality'symmetry of this interaction. Starting from the Fierztransform of the two-flavour 't Hooft interaction (afour-fermion Lagrangian with AS tensor interaction termsaugmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalarinteraction responsible for dynamical symmetry breaking andquark mass generation), we find the following.(a) Four antisymmetrictensor and four AS pseudotensor bosons exist which satisfy amass relation previously derived for scalar and pseudoscalarmesons from the 't Hooft interaction. (b) Antisymmetrictensor bosons mix with vector bosons via one-fermion-loopeffective couplings so that both kinds of bosons have theirmasses shifted and the fermions (quarks) acquire anomalousmagnetic moment form factors that explicitly violate chiralsymmetry. (c) The mixing of massive AS tensor fields withvector fields leads to two sets of spin-1 states. Thesecond set of spin-1 mesons is heavy and has not beenobserved. Moreover, at least one member of this second setis tachyonic, under standard assumptions about the source andstrength of the AS tensor interaction. The tachyonic statealso shows up as a pole in the space-like region of the electromagneticform factors. (d) The mixingof axial-vector fields withantisymmetric tensor bosons is proportional to the (small)isospin-breaking up-down quark mass difference, so themixing-induced mass shift is negligible. (e) The AS tensor versionof the Veneziano-Witten UA(1) symmetry-breakinginteraction does not lead to tachyons, or any AS tensor fieldpropagation to leading order in NC.