Flavor symmetry and mass-splitting formulas for the sub-SU(3) Skyrmion in SU(N)

New mass-splitting formulas for the octet and decuplet baryons are obtained in the sub-SU(3) Skyrme model in SU(N) with N=3 to 8 by the perturbative treatment. The higher-order-term contributions to the perturbative expansions are examined. We find that N=5 or 6 makes the mass spectrum most compatible with data. They are much better than the pure SU(3) model. Some useful Clebsch-Gordan coefficients of SU(N) with N=3, 4, 5, 6, 7, and 8 are calculated and listed.