Current Algebras, Regge Poles, and the Isovector Anomalous Magnetic Moment of the Nucleon

We discuss the sum rule for the isovector anomalous magnetic moment of the nucleon ${{F}_{2}}^{V}(0)=1.85$, which is obtained from the current commutation relation $\ensuremath{\delta}({x}_{0})[{{A}_{0}}^{+}(x), {{A}_{\ensuremath{\nu}}}^{\ensuremath{-}}(0)]=2{{V}_{\ensuremath{\nu}}}^{3}(x){\ensuremath{\delta}}^{4}(x)$ by use of the covariant method proposed by Fubini. We find that (1) the sum rule cannot be evaluated without explicit knowledge of one of the axial-vector-nucleon "scattering" amplitudes; (2) calculating the contributions from the ${P}_{33}(1236)$ and ${D}_{13}(1525)$ using a dispersion-pole model of the weak amplitude gives only ${{F}_{2}}^{V}(0)=0.37$, and (3) estimating the high-energy continuum contribution to the sum rule from Reggepole fits to $\ensuremath{\pi}p$ charge-exchange scattering increases the result to ${{F}_{2}}^{V}(0)\ensuremath{\cong}1.0$. It seems that the sum rule is dominated by low- and high-energy continuum contributions, which must be more accurately known before the validity of the sum rule can be judged.