Effects of theρMeson on Nucleon Form Factors

The isovector charge and anomalous magnetic moment form factors of the nucleon are calculated assuming that the low-energy part of the spectral function is determined by the two-pion intermediate state and the high-energy part of the spectral function can be represented by a subtraction constant. The results are compared with experimental analysis in the form of a pole plus a subtraction constant for each form factor. The spectral function is given in terms of the pion form factor ($2\pi \to \gamma$) and the $N\overline{N}\to 2\pi$ amplitudes. The phase of $2\pi \to \gamma$ as well as $N\overline{N}\to 2\pi$ are determined in terms of $\pi \pi$ $p$-wave phase shift which is adjusted to fit the observed $\rho$-resonance with a mass of 760 MeV and a full width of ∼130 MeV. In the calculation of the $N\overline{N}\to 2\pi$ amplitudes, the exchange of a nucleon and a (3-3) resonance are included as Regge poles. Two parameters are introduced in the Regge pole description. These parameters are adjusted to fit two constants $a_1$ and $a_2$ obtained from the experimental analysis of the form factors. The effective mass of the two-pion state which results from the present calculation is approximately 600 to 650 MeV (well below the $\rho$ mass), in good agreement with the experimental determination.