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/dQ^2, the angular distribution dσ/dΩ_Δ, and the total scattering cross section σ(E_e) 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(E_e) is found to be of the order of 10^-39 cm^2 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 10^38-10^39 cm^-2 sec^-1, makes it possible to observe the weak charged current production of Δ(1232) and determine the axial vector form factors C_i^A (Q^2); (i=3-5). The sensitivity of the differential cross section dσ/dQ^2 to the subdominant form factors C_3^A(Q^2) and C_4^A (Q^2) is found to be strong enough, especially in the low Q^2 region, which can be used to determine them phenomenologically and to test the various theoretical models proposed to calculate them.