Asymptotic Relations among Vector and Axial-Vector Form Factors

We have investigated the constraints that current algebra and partial conservation of axial-vector current impose on the asymptotic behavior of axial-vector and vector form factors in the context of Fubini, Furlan, de Alfaro, and Rossetti's mass extrapolation formalism. We have obtained, first, relations for the nucleon-vector and axial-vector form factors as the four-momentum transfer $t\to -\infty$, in terms of electroproduction amplitudes of infinite photon mass. We have subsequently eliminated these unknown electroproduction amplitudes by means of a link to a higher point function. In so doing, we have been successful in expressing these unknown amplitudes in terms of amplitudes whose behavior asymptotically is given by Regge theory, multiplied by known form factors. This approach has yielded the following relations among form factors, valid as $t\to -\infty :G_A\mathrm{}\left(t\right)=G_A\mathrm{}\left(0\right)\mathrm{}G_M^{}{}_{}{}^V\mathrm{}\left(t\right)\mathrm{}$ and $\frac{G_E^{}{}_{}{}^V\mathrm{}\left(t\right)\mathrm{}}{G_M^{}{}_{}{}^V\mathrm{}\left(t\right)\mathrm{}}\to 0$. A critical discussion of the limit $t\to -\infty$ is also included.