Understanding the nature of the $Δ(1600)$ resonance
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arXiv
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| Format: | Preprint |
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2024
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| author | Hockley, Liam Abell, Curtis Leinweber, Derek Thomas, Anthony |
| author_facet | Hockley, Liam Abell, Curtis Leinweber, Derek Thomas, Anthony |
| contents | We present a coupled-channel analysis of the $ J^P = 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 $ πN \to πN $ 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 $ 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 $ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Understanding the nature of the $Δ(1600)$ resonance Hockley, Liam Abell, Curtis Leinweber, Derek Thomas, Anthony High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory We present a coupled-channel analysis of the $ J^P = 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 $ πN \to πN $ 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 $ 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 $ 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. |
| title | Understanding the nature of the $Δ(1600)$ resonance |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2406.00981 |