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

Abstract

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 Lüscher'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.

Comments: 29 pages, 20 figures