General fermion triangle amplitude in the coupling of spin-1 particles and ward identities

Abstract

The general off mass-shell one-loop amplitude for the fermion triangle diagrams is calculated, in theories with $\gamma_5$ couplings for spin-1 particles. Properties of the Bose symmetry and Ward identities for the couplings of neutral particles are investigated. The V V A and A A A triangle diagrams are obtained from our general form. All resulting amplitudes are consistent with Ward identities. The amplitude for the coupling of three identical spin-1 particles is given. This amplitude obeys Bose symmetry and Ward identities for anomaly free theory.