Extension of the Regge Representation

Abstract

The Regge formula is modified in such a way as to exhibit the "full" contribution of each Regge pole to the scattering amplitude. In this modified form both the contribution from each pole and the new background term have the correct cuts in the $z$ plane. In the case where the partial wave amplitude is meromorphic in the whole $l$ plane we show that, under certain assumptions, the scattering amplitude can be represented by a series sum of contributions from the Regge poles. Each contribution has the correct cut in the $z$ plane, and the series converges for all $z$ in the cut plane. An approximation of the scattering amplitude at low energies in terms of a few contributions from leading poles is discussed. Finally, it is shown that this modified Regge formula leads to a relatively simple bootstrap procedure for constructing the scattering amplitude from unitarity and analyticity.