Bounds on elastic absorptive parts

Abstract

We reduce the general problem of obtaining bounds on elastic absorptive parts of a scattering amplitude subject to unitarity restrictions and any number of constraints involving partial wave amplitudes linearly to a form where it can be directly applied to any such problem. A series of bounds on absorptive parts for positive momentum transfer square t, within the Lehmann-Martin ellipse, is derived. These involve a knowledge of the first few momentum transfer derivatives of the absorptive part in the forward direction, i.e., t = 0. Upper and lower bounds on the higher t-derivatives of the absorptive part at t = 0 are also given.