A description of the ratio between electric and magnetic proton form factors by using space-like, time-like data and dispersion relations

Abstract

We define and use a dispersive technique, based on data, analyticity and dispersion relations to handle the nucleon form factors. We use the available information on the ratio between the electric and magnetic proton form factors, coming from recent space-like and time-like data and theory, as inputs in a dispersive approach that gives as outcome a complex description of this ratio, valid in the whole q 2 plane. The possibility of extending this definition outside the data regions allows us to make predictions about the time-like polarizations, the asymptotic behaviour and the presence of zeros for the ratio.