Baryon resonances in large $N_c$ QCD

The current status and open challenges of large $N_c$ QCD baryon spectroscopy are reviewed. After introducing the $1/N_c$ expansion method, the latest achievements for the ground state properties are revisited. Next the applicability of this method to excited states is presented using two different approaches with their advantages and disadvantages. Selected results for the spectrum and strong and electromagnetic decays are described. Also further developments for the applicability of the method to excited states are presented, based on the qualitative compatibility between the quark excitation picture and the meson-nucleon scattering picture. A quantitative comparison between results obtained from the mass formula of the $1/N_c$ expansion method and quark models brings convincing support to quark models and the implications of different large $N_c$ limits are discussed. The SU(6) spin-flavor structure of the large $N_c$ baryon allows a convenient classification of highly excited resonances into SU(3) multiplets and predicts mass ranges for the missing partners.

Figure 1

A gluon in the traditional and double line notations.

Figure 2

The gluon vacuum polarization diagram in the standard (left) and double line notations of ’t Hooft (right).

Figure 3

Leading-order diagrams for the scattering $B+\pi \to B+\pi$.

Figure 4

Comparison between the quark model and large $N_c$ results for $c_1^2$ (${\mathrm{GeV}}^2$) as a function of the band number $N$. The dotted line represents the quark model mass equation (43) with the parameters (44) from [21] and the points with error bars indicate large $N_c$ results: at $N=0$ the value of $c_1$ was from Eq. (22), at $N=1$ from [134], at $N=2$ from [76] describing the multiplet $[\mathbf{56},2^{+}]$ (see Table 1), at $N=3$ from [136], fit 3 corresponding to the multiplets $[\mathbf{70},{\ell }^{-}]$ ($\ell =1,2,3$), and at $N=4$ from [126] describing the multiplet $[\mathbf{56},4^{+}]$ (see Table 1).