A theory of baryon resonances at large N_c

TL;DR

This paper develops a theoretical framework for baryon resonances at large N_c, deriving their hierarchy of scales and classifying resonances, which aligns well with observed spectra despite N_c being only three.

Contribution

It introduces a new theory of baryon collective excitations based on mean field and large N_c expansion, unifying relativistic and non-relativistic classifications.

Findings

Hierarchy of baryon resonance scales established

Classification reduces to SU(6) in symmetric limit

Good agreement with observed spectra up to 2 GeV

Abstract

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 an hierarchy of scales: The crude mass is O(N_c), 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/N_c). 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 N_c is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.