Baryon decays to radially excited states in the quark model

We have examined the pionic decays of baryon resonances to the first radial excitation of the nucleon ground state in the relativistic quark model of Feynman, Kislinger, and Ravndal. Identifying this state with the $P_{11}$ $N^{*}\mathrm{}\left(1470\right)\mathrm{}$ resonance first suggested by Roper, we find that most of the predicted widths are small. While the experimental data is meager, a recent three-body phase-shift analysis of the $N\pi \pi$ final state between 1450 and 1700 MeV total mass by the Imperial College-Rutherford Laboratory group allows a more detailed study of this region. They find a very strong effect in the final $P_{33}$ state of $N^{*}\pi$; this ${\Delta }^{*}\mathrm{}\left(1690\right)\mathrm{}$ could well be the radial excitation of the ground state $\Delta \mathrm{}\left(1236\right)\mathrm{}$. However, the quark-model prediction of this decay gives a result 3 times smaller in amplitude than the experimental effect. Possible reasons for this are discussed.