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Pion-nucleon scattering in baryon chiral perturbation theory combined with the 1/Nc expansion

D. Jayakodige1,* and J. L. Goity1,2,†

  • *Contact author: dulitha@jlab.org
  • †Contact author: goity@jlab.org
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Phys. Rev. D 112, 114048 – Published 31 December, 2025

DOI: https://doi.org/10.1103/xbrd-8p5x

Abstract

This work implements the combined baryon chiral perturbation theory (BChPT) and 1/Nc expansions for pion-nucleon elastic scattering. The effective theory is based on the baryon sector dynamical spin-flavor SU(4) symmetry emergent in the large Nc limit, whose breaking is controlled by the 1/Nc expansion. The noncommutativity of the chiral and 1/Nc expansions in unitarity corrections (loops) requires a linking of both expansions. As it was shown in the case of baryon masses and currents, the natural linking is the ξ expansion, in which O(p)=O(1/Nc)=O(ξ). The spin-flavor symmetry requires that the ground state baryons span an SU(4) symmetric irreducible representation which implies that in particular N and Δ are active degrees of freedom in the effective theory. The scattering amplitude is expanded to the next-to-next-to leading order in the ξ expansion, corresponding to the one-loop contributions with the leading-order Lagrangian. The results are given for generic Nc in order to demonstrate the consistency of the framework. The spin-flavor symmetry plays a central role in maintaining the consistency of the effective theory with respect to the 1/Nc expansion. This consistency manifests itself in an improvement in the convergence of the low energy expansion with respect to the case of the ordinary BChPT without an explicit dynamical Δ, which is known to be inconsistent with the constraints of Nc scaling. Fits to the πN→πN, S, P, and D partial wave amplitudes from the SAID data base are finally used to test the framework and to determine the energy range of its applicability.

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Phys. Rev. D 112, 114048– Published 31 December, 2025
  • Received 11 June 2025
  • Accepted 1 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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