Threshold Kinematic Constraints and Correlations of Helicity Amplitudes

Abstract

The threshold kinematic constraints and correlations (relations for all helicity amplitudes in terms of one "reduced" helicity-independent amplitude and a given helicity-dependent coefficient) of helicity amplitudes are derived from the threshold behavior of partial-wave amplitudes for any mass and spin combination. Total spin helicity amplitudes are found to be the natural helicity combination for threshold behavior. The pseudothreshold kinematic properties are found to be similar to those at the direct threshold if the total spin helicity amplitudes are modified by appropriate sign changes in their defining linear combinations. The threshold correlations are related to kinematic-singularity-free helicity amplitudes.