Pion-Nucleon Scattering in Combined BChPT and 1/Nc Expansion

Pion–nucleon scattering serves as an essential probe of the strong interaction in the low-energy regime. This study examines pion–nucleon scattering within a combined framework of Baryon Chiral Perturbation Theory (BChPT) and the 1/Nc expansion. The corresponding effective Lagrangian exhibits chiral SU_L(2) × SU_R(2) and spin–flavor SU(4) symmetries in the chiral and large-Nc limits. The power-counting schemes of the chiral and 1/Nc expansions are connected through the ξ expansion, defined such that O(ξ) = O(p) = O(1/Nc). Scattering amplitudes are computed up to O(ξ^3), corresponding to next-to-next-to-leading order, and the renormalization of the effective Lagrangian is performed to the same order. The inclusion of spin-3/2 baryons within this formalism naturally improves convergence. Theoretical predictions for partial waves and phase shifts are compared with experimental data from the SAID database to assess the validity and applicable energy range of the framework. Even at higher energies, the analysis shows excellent agreement with experimental data, especially for the P33 partial wave.