Threshold Electropion Production from Current Algebra and Partially Conserved Axial-Vector Current

Threshold electropion production on nucleons, $e+N\to e+N+\pi$, is studied by current-algebra techniques using the hypothesis of partially conserved axial-vector current, which have proved useful in describing low-energy meson-baryon elastic scattering and photopion production on nucleons. The electric and longitudinal multipole moments $E_{0+}$ and $L_{0+}$ are calculated at threshold in terms of the form factors of the electromagnetic and weak axial-vector currents. The experimental upper bounds on the slope of the differential cross section as a function of $\left|\mathbf{q}\right|$, the momentum in the $\pi N$ c.m. system, i.e., $\left(\frac{1}{\left|\mathbf{q}\right|}\right)\left(\frac{d^2\sigma }{d\Omega d{S_{20}}^L}\right)$, where ${S_{20}}^L$ is the laboratory energy of the final electron, are sufficiently strong to relate the form factors for various values of $-k^2$, the momentum transfer squared of the electrons. More precisely, in this way one can relate the neutron charge form factor ${G_e}^n\left(k^2\right)$ to normalized axial-vector form factor $F_A\left(k^2\right)$. If one takes $F_A\left(k^2\right)$ to have the dipole form $F_A\left(k^2\right)={(1+\frac{k^2}{{M_A}^2})}^{-2\mathrm{}}$ with ${M_A}^2=1.42\mathrm{}$ Be${\mathrm{V}}^2$, which is given by arguments based on chiral $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ and consistent with recent neutrino experiments, then the resulting values of ${G_e}^n\left(k^2\right)$ in the range considered, $0.2\le k^2\le 0.6 \mathrm{Be}{\mathrm{V}}^2$, are consistent with information about ${G_e}^n\left(k^2\right)$ from electron-deuteron and thermal-neutron-electron scattering.