Towers of positive parity excited baryons and their mixing in the large $N_c$ limit

Abstract

We consider configuration mixing for the nonstrange positive parity excited baryons in the $[56^{\prime },0^{+}],[56,2^{+}],[70,0^{+}]$ and $[70,2^{+}]$ quark model $SU(6)\times O(3)$ multiplets contained in the $N=2$ band. Starting from the effective mass operator for these states we show by an explicit calculation that in the large $N_c$ limit they fall into six towers of degenerate states labeled by $K=0,1,1^{\prime },2,2^{\prime },3$. We find that the mixing of the quark model states is much simpler than what is naively expected. To leading order in $N_c$ only states carrying the same $K$ label can mix, which implies that for the spin-flavor states we started with configuration mixing can be parameterized by just two constants, ${\mu }_{K=1}$ and ${\mu }_{K=2}$.

Comments: 26 pages, 4 Tables, corrected references to Eqs.(3,4,5)