Understanding the nature of the $\Delta(1600)$ resonance

We present a coupled-channel analysis of the $ J^P = 3/2^+ \Delta $-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 $ \pi N \to \pi 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 $ \Delta(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 $ \Delta(1600) $ resonance. We find the dominant contributions to this resonance come from strong rescattering in the $ \pi N $ and $ \pi \Delta $ channels. This contrasts the long-held view of a dominant quark model-like core for the $ \Delta(1600) $. Further discussion of other contemporary lattice results for the $ \Delta $ spectrum and $ \pi N $ scattering states is also presented.
Comment: 29 pages, 20 figures