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

Threshold electropion production on nucleons, e+N→e+N+π, 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 E₀₊ and L₀₊ 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 |q|, the momentum in the πN c.m. system, i.e., (1/|q|)(d²σdΩdS₂₀L), where S₂₀L is the laboratory energy of the final electron, are sufficiently strong to relate the form factors for various values of -k², the momentum transfer squared of the electrons. More precisely, in this way one can relate the neutron charge form factor Gₑⁿ(k²) to normalized axial-vector form factor FA(k²). If one takes FA(k²) to have the dipole form FA(k²)=(1+k²MA²)^-2 with MA²=1.42 BeV², which is given by arguments based on chiral SU(2)×SU(2) and consistent with recent neutrino experiments, then the resulting values of Gₑⁿ(k²) in the range considered, 0.2≤k²≤0.6 BeV², are consistent with information about Gₑⁿ(k²) from electron-deuteron and thermal-neutron-electron scattering.