Covariant Approach to Kinematic Constraint Relations for Helicity Amplitudes

Abstract

With the aid of a covariant spin formalism, the kinematic constraint equations for helicity amplitudes are studied in a systematic way for all mass configurations, including the case of zero-mass particles. The complete set of constraints a t thresholds and pseudothresholds is given in a form convenient for calculation; that is, the coefficients of the helicity amplitudes are simple numerical ones (as opposed, for instance, to D functions). For nonzero-mass particles, the reduction of the constraints in terms of total spin amplitudes is shown to follow. Amplitudes with different values of total spin are not related a t thresholds or pseudothresholds.'A partial list of recent works would include Refs. 2-10, other works can be traced from them.

Spectral representation foru- andt-channel exchange processes in a partial-wave decomposition

“…In the literature such a decomposition has been worked out explicitly for various reactions [35,[37][38][39][40][41].…”

“…where we insist on invariant amplitudes, F n (s, t, u), that are free of kinematical constraints [34][35][36]. Owing to energy and momentum conservation the scattering amplitude T ( k, k; w) depends on three 4-vectors kµ , k µ and w µ only with…”