Consistency Questions Raised by Simultaneous Mandelstam and Angular-Momentum analyticity

Abstract

As the result of a study to determine a Reggepole formula with Mandelstam analyticity for the elastic scattering of two unequal-mass particles, we were led to raise the following question: What are the constraints, if any, that follow from assuming that scattering amplitudes satisfy both the Mandelstam representation and the condition of meromorphism in the right-half angular momentum plane? To put it another way, are Mandelstam and l-plane analyticity necessarily consistent in every case? We find that if there is to be consistency, one can conclude directly that the high-energy limit of the Regge-pole position, α(∞), is necessarily negative.