Extrapolation of Nucleon Form Factors. II

Abstract

The magnetic isoscalar form factor is fitted with two poles: the $\ensuremath{\omega}$ and the $\ensuremath{\varphi}$ resonance. The magnetic isovector form factor ${G}_{\mathrm{MV}}$ for spacelike and timelike momentum transfers is fitted using the conformal-transformation techniques of Levinger, Peierls, and Wang, and these techniques are tested using artificial data. If we do not assume a contribution from the $\ensuremath{\rho}$ resonance, we find a spectral function with a broad peak some 100 MeV below the position of the $\ensuremath{\rho}$, and with a negative dip around 1200 MeV. If we assume that the $\ensuremath{\rho}$ resonance contributes additively at its known position and width, but with an adjustable coefficient for its strength, we argue that the $\ensuremath{\rho}$ contributes about 90% of the static moment. The complete spectral function shows a shoulder around 500 MeV, and again a negative dip around 1200 MeV. If we assume that ${G}_{\mathrm{MV}}$ is a product of the form factor for the $\ensuremath{\rho}$ and an adjustable function, we find that the spectral function has a high peak near the $\ensuremath{\rho}$ resonance, and a marked negative dip at 900 MeV. The $\ensuremath{\rho}$ again contributes some 90% of the static moment. The different phenomenonological fits are in semiquantitative agreement with each other and with the recent field-theoretical calculations of Furuichi et al.