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

摘要

We consider configuration mixing for the nonstrange positive parity excitedbaryons in the $[\mathbf{56'},0^+],[\mathbf{56},2^+], [\mathbf{70},0^+] $ and$[\mathbf{70},2^+]$ quark model $SU(6) \times O(3)$ multiplets contained in the$N=2$ band. Starting from the effective mass operator for these states we showby an explicit calculation that in the large $N_c$ limit they fall into sixtowers of degenerate states labeled by $K=0,1,1',2,2',3$. We find that themixing 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 configurationmixing can be parameterized by just two constants, $\mu_{K=1}$ and $\mu_{K=2}$.