A New Sum Rule for N Scattering and the Regge Pole Model

Abstract

A new sum rule of superco!lvergent type is derived for the rcN heJicity-nonflip amplitude and is examined experimentally. It is found that the sum rule is well satisfied under the assumption of the P- and P'-Regge pole dominance model. I~ecently the Regge pole model is used to obtain the sum rules of super­ convergent type for various amplitudes. 1 ),2) In this paper \ve propose a sum rule for the pion-nucleon helicity-nonflip elastic amplitude, and examine it ex­ perimentally. Under the assumption of the P- and P'-Regge pole dominance model at high energy, it is found that our sum rule is well satisfied and therefore we can conclude the validity of the Regge pole dominance model even though we cannot exclude the possibility of the existence of other singularities, e.g. the Regge cuts if the discontinuities are reasonably small. L,et us start from the forward helicity-nonflip elastic amplitude