Understanding the nature of the Δ(1600) resonance

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 experimentally measured π N → π N scattering observables. In the same vein as L\"{u}scher's approach, we then connect this infinite-volume inspired Hamiltonian with finite-volume lattice QCD results. Drawing on lattice correlation-matrix eigenvectors identifying the $ 1s $ and $ 2s $ states in the finite-volume Δ(3/2⁺) spectrum, and utilising 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 π N and π Δ 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 π N scattering states is also presented.