Weak and Electroproduction of Nucleon Resonances in the Harmonic-Oscillator Quark Model

Abstract

Using the model that the baryons are composed of quarks with harmonic interactions, we compute cross sections for high-energy neutrinos and electrons to excite the nucleon to the resonance states with masses below 1.9 GeV. The frame dependence of the nonrelativistic quark-model results is emphasized and discrepancies between some previous model calculations of electroproduction form factors and data are shown to be due to the frame chosen. For neutrino production, the model predicts that a significant excitation of the second and third resonance regions will be seen from neutrons, but with proton targets only the $\Delta \mathrm{}\left(1236\right)\mathrm{}$ excitation will be observed. An interesting result of the electroproduction calculation is the prediction that the $P_{11}\mathrm{}\left(1470\right)\mathrm{}$, while suppressed at small $t$ (and hence in photoproduction), will dominate over the $S_{11}\mathrm{}\left(1550\right)\mathrm{}$ and $D_{13}\mathrm{}\left(1520\right)\mathrm{}$ at large $t\gtrsim 1.5{\left(\frac{\mathrm{GeV}}{c}\right)}^2$.