A complete unitary representation for the residue function β and asymptotic behavior of Im α

Abstract

The unitary Cheng representation for partial wave amplitudes in terms of Reggetrajectories is used to derive a new unitary representation for the residue functionβ(s), which allows to evaluateβ(s) for all values ofs, especially for negative values. The discussion of both representations gives three different arguments that Imα(s) has to decrease exponentially ass increases. The new formula also allows to establish a unitary bootstrap system forβ(s) and Imα(s).