At large number of colors, $N_c$ quarks in baryons are in a mean field of definite space and flavor symmetry. We write down the general Lorentz and flavor structure of the mean field, and derive the Dirac equation for quarks in that field. The resulting baryon resonances exhibit a hierarchy of scales: the crude mass is $\mathcal{O}(N_c)$, the intrinsic quark excitations are $\mathcal{O}(1)$, and each intrinsic quark state entails a finite band of collective excitations that are split as $\mathcal{O}(1/N_c)$. We build a (new) theory of these collective excitations, where the full dynamics is represented by only a few constants. In a limiting (but unrealistic) case when the mean field is spherically and flavor symmetric, our classification of resonances reduces to the SU(6) classification of the old nonrelativistic quark model. Although in the real world $N_c$ is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.

• Received 9 August 2013

DOI:https://doi.org/10.1103/PhysRevD.88.074030