Configuration Mixing of Quark States in Baryons

Abstract

Mixing angles are used to describe the $SU(6)\otimes O(3)$ symmetry breaking in $\left[70,~1^-\right]$ multiplet in the sector of the lowest mass nucleon resonances, which are investigated extensively in constituent quark models for baryon spectroscopy. The transition amplitudes for the meson photoproduction off nucleon can also be expressed in terms of the mixing angles to take into account the configuration mixing. Those amplitudes are derived as a function of the mixing angles between $|N^2P_M{J}^-\rangle$ and $|N^4P_M{J}^-\rangle$ states, with $J$=1/2 and 3/2, for the processes $\gamma p \to \eta p,~K^+ \Lambda,~K^+ \Sigma^\circ,~K^\circ \Sigma^+$. The present status of our knowledge on the mixing angles between $S_{11}(1535)$ and $S_{11}(1650)$ ($\theta _{S}$), as well as between $D_{13}(1520)$ and $D_{13} (1700)$ ($\theta _{D}$) is reported. Since these resonances play very important role in the threshold region for both $\eta$ and kaon production mechanisms, they are expected to provide crucial tests of different quark models for the baryon spectroscopy.