All you need isN: Baryon spectroscopy in two largeNlimits

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 ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit places quarks in the fundamental representation of $\mathrm{SU}({N}_{c})$, 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.