A dispersion theoretical calculation of inelastic contributions to the nucleon isovector form factors

Abstract

We calculate the contribution of the ππ, π 0 ω and ϱϵ intermediate statesto the isovector nucleon form factors F i v( q 2) in the space- and time-like region using dispersion relations together with unitarity. In the space-like region good agreement with the existing data is found, i.e. we are able to explain the difference in the behaviour of F 1 v which decreases like 1/ q 2 and F 2 v which shows a dipole-like fall-off for q 2 < 0. This is due to the π 0 ω contribution which is rather small for F 1 v but gives a large negative contribution in the spectral function for F 2 v. Also the anomalous magnetic moment is found to be dominated by the ππ and π 0 ω contributions. In the time-like region beyond the N N threshold our method is not sufficient. First, we neglected the N N intermediate which certainly is important in this region. Second, the existing data of the various meson form factors in the time-like region and the necessary coupling constants are not known with sufficient accuracy.