Charged current weak production of $\Delta(1232)$ induced by electrons and positrons

TL;DR

This study analyzes the weak production of the $
232$ resonance by electrons and positrons at intermediate energies, providing cross sections and exploring the potential to measure axial form factors with high-luminosity beams.

Contribution

It offers the first detailed calculations of differential and total cross sections for electron/positron induced $
232$ production and discusses how these can be used to determine axial form factors.

Findings

Cross sections are around 10^{-39} cm^2 at a few GeV energies.

High luminosity electron/positron beams enable observation of $
232$ production.

Differential cross sections are sensitive to subdominant axial form factors.

Abstract

The charged current weak production of $\Delta (1232)$ 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 $\frac{d\sigma}{dQ^2}$, the angular distribution $\frac{d\sigma}{d\Omega_{\Delta}}$, and the total scattering cross section $\sigma(E_e)$ 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 $\sigma(E_e)$ 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 $\Delta(1232)$ and determine the axial vector form factors $C_{i}^{A} (Q^2);~(i=3-5)$. The sensitivity of the differential cross section $\frac{d\sigma}{dQ^2}$ 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.