Charged current weak electroproduction of Delta resonance

We study the weak production of $Δ$ (i.e. $e^{-} + p \to Δ^{0}+ ν_{e}$ and $e^{+} + p \to Δ^{++} + \barν_{e}$) in the intermediate energy range corresponding to the Mainz and TJNAF electron accelerators. The differential cross sections $σ(θ)$ are found to be of the order of $10^{-39}$ cm$^2$/sr, over a range of angles which increases with energy. The possibility of observing these reactions with the high luminosities available at these accelerators, and studying the weak N-$Δ$ transition form factors through these reactions is discussed. The production cross section of N$^*(1440)$ in the kinematic region of $Δ$ production is also estimated and found to be small.

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