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 F₂V(0)=1.85, which is obtained from the current commutation relation δ(x₀)[A₀⁺(x), A_ν^-(0)]=2V_ν³(x)δ⁴(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 P₃₃(1236) and D₁₃(1525) using a dispersion-pole model of the weak amplitude gives only F₂V(0)=0.37, and (3) estimating the high-energy continuum contribution to the sum rule from Reggepole fits to πp charge-exchange scattering increases the result to F₂V(0)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.