Possible Measurement of the Nucleon Axial-Vector Form Factor in Two-Pion Electroproduction Experiments

Current-algebra techniques and the hypothesis of partially conserved axial-vector current are used to derive a low-energy theorem for the reaction $e+N\to e+N+\pi +\pi$ (soft). Particular attention is paid to satisfying the requirements of gauge covariance. Except for recoil corrections, the resulting matrix element is proportional to the nucleon axial-vector form factors, and we suggest that this electromagnetic process may be used to measure $g_A\left(k^2\right)$.