Use of $SU(3)$ flavor projection operators to construct baryon-meson scattering amplitudes in the $1/N_c$ expansion

An $SU(3)$ flavor projection operator technique is implemented to construct the baryon-meson scattering amplitude in the framework of the $1/N_c$ expansion of QCD, where $N_c$ is the number of color charges. The operator technique is implemented to evaluate not only the lowest-order scattering amplitude but also effects coming from first-order perturbative $SU(3)$ flavor symmetry breaking and strong isospin breaking. The most general expression is obtained by accounting for explicitly the effects of the decuplet-octet baryon mass difference. At order $\mathcal{O}(1/N_c^2)$, a large number of unknown operator coefficients appear, so there is little additional predictive power unless leading and subleading terms are retained. Although the resultant expression is general enough that it can be applied to any incoming and outgoing baryons and pseudo scalar mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $Nπ\to Nπ$ scattering processes are explicitly dealt with.