All you need is N: Baryon spectroscopy in two large N limits

Abstract

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct 1/N_c expansion. The familiar 't Hooft N_c -> \infty limit places quarks in the fundamental representation of SU(N_c), while an alternative approach places quarks in its two-index antisymmetric representation. At N_c=3 these two 1/N_c expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large N_c limit generates an emergent spin-flavor symmetry that leads to the vanishing of particular linear combinations of baryon masses at specific orders in the expansions. Experimental evidence shows that these relations hold at the expected orders regardless of which large N_c limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large N_c limit in which one flavor is taken to transform in the two-index antisymmetric representation and the rest of the flavors are in the fundamental representation. While this hybrid large N_c limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.

8 pages, 3 figures. v3: Published version, one equation corrected

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• Baryons in QCD_{AS} at Large N_c: A Roundabout Approach
• Orbifold equivalence for finite density QCD and effective field theory
• Quantum-Number Exotic Tetraquarks at Large $N_c$ in QCD(AS)
• Baryons and baryonic matter in the large Nc and heavy quark limits
• Bose-Fermi cancellations without supersymmetry
• Spin contribution to light baryons in different large-$N$ limits
• Light baryon masses in different large-$N_c$ limits
• Baryon resonances in large $N_c$ QCD
• Baryon Magnetic Moments in Alternate 1/N_c Expansions
• Alternate 1/N_c Expansions and SU(3) Breaking from Baryon Lattice Results
• Color Superconductivity at Large N: A New Hope
• SU(6)$\supset$SU(3)xSU(2) and SU(8)$\supset$SU(4)xSU(2) Clebsch-Gordan coefficients
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