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 ${\mu }_{K=2}$.

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

References in corpus (10)

• SU(N) gauge theories at large N
• The Flavor Structure of the Excited Baryon Spectra from Lattice QCD
• Lattice study of large $N_c$ QCD
• The Nc dependencies of baryon masses: Analysis with Lattice QCD and Effective Theory
• Baryon resonances in large $N_c$ QCD
• The permutation group S_N and large Nc excited baryons
• Decoupling Spurious Baryon States in the 1/N_c Expansion of QCD
• Baryon spin-flavor structure from an analysis of lattice QCD results of the baryon spectrum
• Operator analysis of effective spin-flavor interactions for L=1 excited baryons
• 1/Nc expansion and the spin-flavor structure of the quark interaction in the constituent quark model

Cited by in corpus (2)

• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Towers of baryons of the $\mathcal{N}=2$ quark model band in the large $N_c$ limit