Pion Nucleon Scattering in BChPT combined with 1/Nc Expansion

Pion–nucleon scattering provides crucial insights into the chiral dynamics of the low energy regime of the strong interactions. In this study, a combined framework of Baryon Chiral Perturbation Theory (BChPT) and the 1/N_c expansion is formulated for analyzing pion–nucleon scattering. The effective Lagrangian of this approach has chiral SU_L(2) × SU_R(2) symmetry and spin–flavor SU(4) symmetry in the chiral and large N_c limits. The power countings of the chiral and 1/N_c expansions are linked through the ξ expansion, defined as O(ξ) = O(p) = O(1/N_c). The scattering cross sections are calculated at the one-loop level, corresponding to the next-to-next-to-leading order in the ξ expansion. The renormalization of the scattering amplitude involves the effective Lagrangian at O(ξ³). This framework shows improved convergence due to the natural inclusion of spin-3/2 baryons, as demanded by the spin-flavor symmetry. The theoretically calculated partial wave scattering amplitudes and corresponding phase shifts are fitted to experimental data from the SAID database, testing the validity and applicable energy range of the framework. The results show improved agreement with the data as compared with other previously analyzed BChPT approaches, in particular in the validity of its range of energy.