Algebra of Currents and Form Factors at Finite Momentum Transfer

Abstract

By using equal-time commutation relations of chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ current components, and the partially conserved-axial-vector-current hypothesis, we derive several relationships among the axial-vector and electromagnetic form factors and the pion electroproduction amplitude at nonzero momentum transfer. In the approximation of retaining only the (3,3) resonance contribution to the pion electroproduction amplitude, we derive an approximate identity of the isovector Dirac charge form factor and the axial-vector form factor. Further sum rules for the isovector and isoscalar Pauli magnetic-moment form factors are obtained which are fairly well satisfied. The form factor for the induced pseudoscalar coupling is discussed.