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

TL;DR

This paper uses Hamiltonian Effective Field Theory to analyze the $ ext{Δ}(1600)$ resonance, combining lattice QCD data and scattering experiments to reveal its dominant meson-baryon rescattering nature rather than a simple quark core.

Contribution

It introduces a coupled-channel HEFT approach that integrates lattice QCD results with experimental scattering data to elucidate the structure of the $ ext{Δ}(1600)$ resonance.

Findings

The $ ext{Δ}(1600)$ resonance is mainly formed by strong rescattering in $ ext{π}N$ and $ ext{π}Δ$ channels.

The study challenges the view of a quark model-like core dominating the $ ext{Δ}(1600)$.

Finite-volume lattice results are connected with infinite-volume scattering states using HEFT.

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 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.