The real part of the elastic scattering amplitude at nonzero transferred momenta

TL;DR

This paper provides a model-independent analysis of the real part of the elastic scattering amplitude at nonzero transferred momenta, revealing sign changes and asymptotic behaviors relevant to experimental observations.

Contribution

It introduces a model-independent method to determine the real part of the elastic scattering amplitude outside the diffraction peak, highlighting its asymptotic properties and sign change behavior.

Findings

The ratio of real to imaginary parts changes sign at a specific transferred momentum.

The asymptotic behavior of the ratio is discussed and characterized.

Comments relate the findings to current experimental data on differential cross-sections.

Abstract

The model-independent solution of the s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak allows to make conclusions about its real part at nonzero transferred momenta. The asymptotical properties of the ratio of the real to imaginary part of the amplitude are discussed. In particular, it is explicitly shown that the ratio changes its sign at a defnite value of the transferred momentum. Some comments concerning the present day experimental results about the behavior of the differential cross-section of elastic scattering outside the diffraction cone are given.