Exotic baryons with charm number $\pm 1$ from the Skyrme model

We illustrate the exotic $\mathrm{SU}\left(3\right)\mathrm{}$ baryon submultiplets in the $\mathrm{SU}\left(4\right)\mathrm{}$ baryon multiplets predicted from the flavor $\mathrm{SU}\left(4\right)\mathrm{}$ collective-coordinate quantization, and investigate the exotic states with charm number $C$ $=\pm 1$ up to leading order of ${1/N}_c$ under chiral ${\mathrm{SU}\left(3\right)\mathrm{}}_L\times {\mathrm{SU}\left(3\right)\mathrm{}}_R$ symmetry and the heavy quark limit from bound state approach. We find that there exist the $\overline{15}$-plets and 24-plets with $C=1\mathrm{}$ and the $6¯$-plets, 15-plets and ${15}^{\prime }$-plets with $C=-1$ bounded in this approach, qualitatively consistent with predictions from the flavor $\mathrm{SU}\left(4\right)\mathrm{}$ collective-coordinate quantization. By fitting one unique parameter of leading $\mathrm{SU}\left(3\right)\mathrm{}$ flavor symmetry breaking term with the mass difference between ${\Xi }_c$ and ${\Sigma }_c$ and up to ${O(m}_Q^0{N}_c^{-1}),$ we give all the average masses of baryons in 6¯-plet and 15-plet. Several general relations of these masses without any parameter are also introduced.