Covariant amplitudes for mesons

Abstract

We show how to construct covariant amplitudes for processes involving higher spins in this paper. First we give the explicit expressions of Rarita-Schwinger wave functions and propagators for bosons with spins, then kinematic singularity free 3-leg effective vertexes are derived and given in a list. Equivalence relations are worked out to get these independent vertexes. Constraints of space reflection symmetry and boson symmetry are considered and shown in a explicit way. Some helicity amplitudes for two-body decays in center of frame are calculated. Finally the covariant helicity amplitudes for the process $a_1\to \pi^+\pi^+\pi^-$ are constructed to illustrate how to include background (1PI) amplitudes. Both background amplitudes and resonance amplitudes are needed to give reliable descriptions to high energy reactions.