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

Jayakodige, D.; Goity, J. L.

doi:10.1103/xbrd-8p5x

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

Journal Article · Wed Dec 31 00:00:00 EST 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/xbrd-8p5x· OSTI ID:3011658

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Hampton Univ., Hampton, VA (United States)
Hampton Univ., Hampton, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

This work implements the combined baryon chiral perturbation theory (BChPT) and 1/𝑁_𝑐 expansions for pion-nucleon elastic scattering. The effective theory is based on the baryon sector dynamical spin-flavor 𝑆⁢𝑈⁡(4) symmetry emergent in the large 𝑁_𝑐 limit, whose breaking is controlled by the 1/𝑁_𝑐 expansion. The noncommutativity of the chiral and 1/𝑁_𝑐 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/𝑁_𝑐) = 𝒪⁡(𝜉). The spin-flavor symmetry requires that the ground state baryons span an 𝑆⁢𝑈⁡(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 𝑁_𝑐 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/𝑁_𝑐 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 𝑁_𝑐 scaling. Fits to the 𝜋⁢𝑁 → 𝜋⁢𝑁, 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.

View Accepted Manuscript (DOE)

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 3011658

Report Number(s):: DOE/OR/23177--7870; JLAB-THY--25-4343; arXiv:2506.05224

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 11 Vol. 112; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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