A model for pion Delta electroproduction on the proton

Abstract

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.

Comments: 30 pages, 10 figures (ps files). Major changes added. To be published in Nucl. Phys. A