Dispersion relations provide a powerful tool to analyze the electromagnetic form factors of the nucleon for all momentum transfers. Constraints from meson-nucleon scattering data, unitarity, and perturbative quantum chromodynamics (QCD) can be included in a straightforward way. In particular, we include the $2\pi ,\rho \pi$, and $K\overline{K}$ continua as independent input in our analysis and provide an error band for our results. Moreover, we discuss two different methods to include the asymptotic constraints from perturbative QCD. We simultaneously analyze the world data for all four form factors in both the spacelike and timelike regions and generally find good agreement with the data. We also extract the nucleon radii and the $\omega \mathit{NN}$ coupling constants. For the radii, we generally find good agreement with other determinations with the exception of the electric charge radius of the proton, which comes out smaller. The $\omega \mathit{NN}$ vector coupling constant is determined relatively well by the fits, but for the tensor coupling constant even the sign cannot be determined.

• Received 4 September 2006

DOI:https://doi.org/10.1103/PhysRevC.75.035202