Neutron-proton form factors. II

Abstract

In a recent letter we suggested that the momentum dependence of the exact meson propagator may be responsible for the dipole-like behavior of the nucleon electromagnetic form factors over the limited range of data available. In this paper we extend the analysis to include more than one vector-meson propagator, and, by assuming a simplified form for the imaginary part of the level shift, we calculate the form factors explicitly. The nucleon electromagnetic form-factor data are fitted for momentum transfer to $2\frac{\mathrm{GeV}}{c}$ assuming just one isovector-vector meson and two isoscalar-vector mesons. The resulting fit is much better than that obtained using the dipole formula, and min ${\ensuremath{\chi}}^{2}$ occurs for values of the masses and widths of the vector mesons close to the experimental values of the $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\phi}$ resonances. The six independent meson-nucleon coupling constants are determined. Their values are consistent with the assumption that the nucleon charge and the magnetic moment distributions are extended, that is, that there are no hard-core contributions to the form factors. This assumption completely determines the isovector coupling constants and reduces the number of independent coupling constants to two. The pion and kaon charge form factors, as deduced from the nucleon charge form factors assuming universality, are compared with the available data. The pion form factors fit the data in both the spacelike and the timelike regions, including the resonance shape for the $\ensuremath{\rho}$ contribution to the pion form factor. The kaon form-factor data disagree with the assumption of universality in both the spacelike and timelike regions.