The unitary equation in a fixed momentum transfer representation

Abstract

An extension of the fixed momentum transfer representation for an S-matrix representation of elementary particles is developed. In this representation it is postulated that a function S U (2) on the second sheet can be found such that the matrix product S S U (2) is analytic everywhere in a complex energy plane, and S U (2) is a continuation of S ∗ in the neighborhood of the right-hand cut. The problem of π +p scattering is considered. The kinematic variables are continued from the physical region to the neighborhood of the Born pole, and the unitary equation is there applied. A function for S U (2) was chosen there with parameters determined by unitarity. Two calculations were made, each with a different choice for the form of S U (2). It is shown how unitarity determines the coupling constant together with the values of the parameters of S U (2). The calculated value of the coupling constant, in both cases, is ∼ 16, in good agreement with experiment.