Understanding the nature of the Δ(1600) resonance

Abstract

We present a coupled-channel analysis of the JP=3/2+Δ-baryon spectrum, based in the framework of Hamiltonian effective field theory (HEFT). We construct a Hamiltonian which mixes quark model-like single-particle states and two-particle meson-baryon channels, and constrain this via phase shifts and inelasticities derived from πN→πN scattering data. In the same vein as Lüscher’s approach, we then connect this infinite-volume inspired Hamiltonian with finite-volume lattice quantum chromodynamics (QCD) results. Drawing on lattice correlation-matrix eigenvectors identifying the 1s and 2s states in the finite-volume Δ(3/2+) spectrum, and utilizing the HEFT eigenvectors describing the composition of the energy eigenstates, we resolve the structure of these states and their relation to the Δ(1600) resonance. We find the dominant contributions to this resonance come from strong rescattering in the πN and πΔ channels. This contrasts the long-held view of a dominant quark model-like core for the Δ(1600). Further discussion of other contemporary lattice results for the Δ spectrum and πN scattering states is also presented. Published by the American Physical Society 2025