Charged current weak production of Δ(1232) induced by electrons and positrons

The charged current weak production of Δ (1232) from the free proton target induced by the electron/positron in the intermediate energy range corresponding to the beam energy available at JLab and Mainz, has been studied. The results for the differential scattering cross section dσ/dQ², the angular distribution dσdΩΔ, and the total scattering cross section σ(Eₑ) for both the electron and positron induced processes are presented, for the various energies in the range of 0.5--4~GeV. The cross section σ(Eₑ) is found to be of the order of 10⁻³⁹~cm² for the electron/positron energies in the few GeV range. The availability of electron/positron beams having well defined energy and direction with very high luminosity of the order of 10³⁸-10³⁹~cm⁻²~sec⁻¹, makes it possible to observe the weak charged current production of Δ(1232) and determine the axial vector form factors CᵢA (Q²);~(i=3-5). The sensitivity of the differential cross section dσ/dQ² to the subdominant form factors C₃A(Q²) and C₄A (Q²) is found to be strong enough, especially in the low Q² region, which can be used to determine them phenomenologically and to test the various theoretical models proposed to calculate them.