Baryon-meson scattering amplitude in the $1/N_c$ expansion
The baryon-meson scattering amplitude is computed within the $1/N_c$ expansion of QCD, where $N_c$ is the number of color charges. The most general expression is obtained by accounting for explicitly the effects of the decuplet-octet baryon mass difference and perturbative flavor $SU(3)$ symmetry breaking. Although the resultant expression is general enough that it can be applied to any incoming and outgoing baryons and mesons, provided that the Gell-Mann--Nishijima scheme is respected, results for $N\pi$ scattering processes are explicitly dealt with. With these, some isospin relations are verified to be valid at the physical value $N_c=3$. The expressions obtained here represent a first effort toward understanding scattering processes in the context of the $1/N_c$ expansion.