Symmetric vertex couplings for all spins and parities

Abstract

Interaction Hamiltonians for three particles having arbitrary spins and parities are constructed based on the rather stringent requirement of permutation symmetry. There are only two free parameters in each Hamiltonian: an overall coupling constant and a scaling parameter (identified as the inverse slope of a Regge trajectory). Vertex functions are evaluated in lowest order purturbation theory and their use in formulating Reggeized scattering amplitudes is reviewed. In the particular case of three normal-parity bosons the calculated vertex functions coincide with the vertices extracted from a 6-point dual resonance amplitude. The results presented here may be used, for example, to predict the two-body decay characteristics of resonances and, in a more theoretic vein, to serve as a base upon which to build dual resonance amplitudes for particles of all spins and parities.