Obtaining real parts of scattering amplitudes directly from cross section data using derivative analyticity relations

Abstract

We show that one can obtain real parts of scattering amplitudes by knowing the imaginary parts at only nearby energies. This is accomplished by re-casting the dispersion integral into an equivalent form which we will calla “derivative analyticity relation”. Predictions are given for forward amplitudes where σ T is measured: pp, p p, K ± p, π ± p, γ p . We deduce the real part of the elastic pp amplitude away from the forward direction at ISR energies.