An alternative approach to baryon masses in the $1/N_c$ expansion of QCD

The baryon mass operator is studied within a combined expansion in $1/N_c$ and perturbative $SU(3)$ flavor symmetry breaking, where $N_c$ denotes the number of quark charges. Flavor projection operators are used to classify the baryon operators involved in the expansion, which fall into the flavor representations $1$, $8$, $10+\overline{10}$, $27$, $35+\overline{35}$ and $64$. This approach allows one to incorporate up to third-order flavor symmetry breaking in the baryon mass operator in a rigorous and systematic way. Previous work on the subject is considered to validate the approach. A fit to data is performed to evaluate the free parameters in the theory and to produce some numerical values of baryon masses. Results are consistent and reaffirm the striking success of the $1/N_c$ expansion.