General classification of conspiracy relations

Abstract

We present a study of constraints on helicity amplitudes when the external particles have arbitrary spins. The reaction πN → ϱN is studied in detail and we find two types of “conspiracy relations”. The first one occurs at t = 0 when the masses of π and ϱ are different; it is different from the Gribov-Volkov type as it vanishes when the masses of π and ϱ are equal. The Gribov-Volkov type of relations is very different from the preceding one and occurs when the masses of π and ϱ are the same. We show how all these relations can be found without explicit reference to the invariant amplitudes and argue that generally all conspiracy relations can be obtained directly from the Trueman-Wick crossing relations between helicity amplitudes.