We performed a complete analysis of the spectrum of all the states in the ${ \cal N}=2$ quark model harmonic oscillator band with $N_f=3$ in the large $N_c$ limit including the often disregarded antisymmetric multiplet $[{ \bf 20},1^+]$. We included configuration mixing effects. We found that the states in the $[{ \bf 56},L^+]$ and $[{ \bf 70},L^+]$ with $L=0,2$ fall into nine towers of degenerate states. We found that nonstrange antisymmetric states fall into three towers and respond to the same structure as the states in the $[{ \bf 70},1^-]$ multiplet. We also showed explicitly the compatibility of these results and the scattering resonance picture.
Categories: nucl-th hep-lat hep-ph