A model for pion Delta electroproduction on the proton

We have extended a model for the $\gamma N\to \pi\pi N$ reaction to virtual photons and selected the diagrams which have a $\Delta$ in the final state. With this model we have evaluated cross sections for the virtual photon cross section as a function of $Q^2$ for different energies. The agreement found with the $\gamma_v p\to\Delta^0\pi^+$ and $\gamma_v p\to\Delta^{++}\pi^-$ reactions is good. The sensitivity of the results to $N\Delta$ transition form factors is also studied. The present reaction, selecting a particular final state, is an extra test for models of the $\gamma_{v} N\to \pi\pi N$ amplitude. The experimental measurement of the different isospin channels for this reaction are encouraged as a means to unravel the dynamics of the two pions photoproduction processes.