Analytical Extension of the Frazer-Fulco Unitarity Relations for Isovector Nucleon Form Factors to the Complex t-Plane

Abstract

The unitarity relations for isovector nucleon form factors in the two-pion approximation for the intermediate states are analytically extended in a model independent way from the real half-axis t > 4 $μ^2$ ($μ$ is the pion mass) to the whole complex t-plane. As a result, the explicit integral representations for the nucleon form factors are constructed in terms of the pion form factor and imaginary parts of the t-channel p-wave piN-scattering amplitudes at t < 0. New method based on the explicit integral representations is developed for numerical evaluation of the two-pion contribution to the isovector nucleon form factors. The results of different methods are compared and their efficiency is discussed.