A Theory of Baryon Resonances at Large N C

At large number of colors, Nc 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 an hierarchy of scales: The crude mass is O(Nc), the intrinsic quark excitations are O(1), and each intrinsic quark state entails a finite band of collective excitations that are split as O(1/Nc). We build a (new) theory of those collective excitations, where 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 non-relativistic quark model. Although in the real world Nc is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.