Ambiguity in the line shape of scattering amplitude

Abstract

The scattering amplitude is typically approximated using some parametrization scheme that can be analytically continued to the complex energy plane, thereby allowing us to determine the nature of enhancement. However, some parametrizations put strong restrictions on the possible number of poles that can be present in different Riemann sheets. We show in this paper that one cannot hastily conclude the nature of enhancement by simply looking at the line shape of only one of the scattering channels. The ambiguity can be addressed if the contribution of the other channels with the same final state is added to the full scattering cross-section.