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

Abstract

Threshold electropion production on nucleons, $e+N\ensuremath{\rightarrow}e+N+\ensuremath{\pi}$, 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 $|\mathbf{q}|$, the momentum in the $\ensuremath{\pi}N$ c.m. system, i.e., $(\frac{1}{|\mathbf{q}|})(\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d{{S}_{20}}^{L}})$, where ${{S}_{20}}^{L}$ is the laboratory energy of the final electron, are sufficiently strong to relate the form factors for various values of $\ensuremath{-}{k}^{2}$, the momentum transfer squared of the electrons. More precisely, in this way one can relate the neutron charge form factor ${{G}_{e}}^{n}({k}^{2})$ to normalized axial-vector form factor ${F}_{A}({k}^{2})$. If one takes ${F}_{A}({k}^{2})$ to have the dipole form ${F}_{A}({k}^{2})={(1+\frac{{k}^{2}}{{{M}_{A}}^{2}})}^{\ensuremath{-}2}$ with ${{M}_{A}}^{2}=1.42$ Be${\mathrm{V}}^{2}$, which is given by arguments based on chiral $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ and consistent with recent neutrino experiments, then the resulting values of ${{G}_{e}}^{n}({k}^{2})$ in the range considered, $0.2\ensuremath{\le}{k}^{2}\ensuremath{\le}0.6 \mathrm{Be}{\mathrm{V}}^{2}$, are consistent with information about ${{G}_{e}}^{n}({k}^{2})$ from electron-deuteron and thermal-neutron-electron scattering.