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

The generalization of QCD to many colors is not unique; each distinct choice corresponds to a distinct 1/Nc expansion. The familiar 't Hooft Nc→a z limit places quarks in the fundamental representation of SU(Nc), while an alternative approach places quarks in its two-index antisymmetric representation. At Nc=3 these two 1/Nc expansions coincide. We compare their predictions for certain observables in baryon spectroscopy, particularly mass combinations organized according to SU(3) flavor breaking. Each large Nc 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 Nc limit one uses, suggesting the validity of either limit in the study of baryons. We also consider a hybrid large Nc 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 Nc limit is theoretically attractive, we show that for a wide class of observables it faces some phenomenological difficulties.