Structure of the $\mathrm{\ensuremath{\Lambda}}(1670)$ resonance

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Structure of the $Λ (1670)$ resonance

Jiong-Jiong Liu, Zhan-Wei Liu, Kan Chen, Dan Guo, Derek B. Leinweber, Xiang Liu, and Anthony W. Thomas

Phys. Rev. D 109, 054025 – Published 18 March 2024

Abstract

We examine the internal structure of the $Λ (1670)$ through an analysis of lattice QCD simulations and experimental data within Hamiltonian effective field theory. Two scenarios are presented. The first describes the $Λ (1670)$ as a bare three-quark basis state, which mixes with the $π Σ$ , $\bar{K} N$ , $η Λ$ and $K Ξ$ meson-baryon channels. In the second scenario, the $Λ (1670)$ is dynamically generated from these isospin-0 coupled channels. The $K^{-} p$ scattering data and the pole structures of the $Λ (1405)$ and the $Λ (1670)$ can be simultaneously described well in both scenarios. However, a comparison of the finite-volume spectra to lattice QCD calculations reveals significant differences between these scenarios, with a clear preference for the first case. Thus the lattice QCD results play a crucial role in allowing us to distinguish between these two scenarios for the internal structure of the $Λ (1670)$ .

Received 21 December 2023
Accepted 26 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.054025

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Hadron-hadron interactions Quark model Strong interaction

Baryons Hadrons

Nuclear PhysicsParticles & Fields

Authors & Affiliations

Jiong-Jiong Liu^1,2,3, Zhan-Wei Liu ^1,2,3,*, Kan Chen^4,5,6,7,8, Dan Guo⁸, Derek B. Leinweber ^9,†, Xiang Liu ^1,2,3,‡, and Anthony W. Thomas ^9,§

¹School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
²Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
³Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, and MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
⁴School of Physics, Northwest University, Xi’an 710127, China
⁵Shaanxi Key Laboratory for theoretical Physics Frontiers, Xi’an 710127, China
⁶Institute of Modern Physics, Northwest University, Xi’an 710127, China
⁷Peng Huanwu Center for Fundamental Theory, Xi’an 710127, China
⁸School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
⁹ARC Special Research Centre for the Subatomic Structure of Matter (CSSM), Department of Physics, University of Adelaide, Adelaide, South Australia 5005, Australia

^*liuzhanwei@lzu.edu.cn
^†derek.leinweber@adelaide.edu.au
^‡xiangliu@lzu.edu.cn
^§anthony.thomas@adelaide.edu.au

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Vol. 109, Iss. 5 — 1 March 2024

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Figure 1
Experimental data [60, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90] for the cross sections of $K^{-} p \to K^{-} p$ , ${\bar{K}}^{0} n$ , $π^{0} Λ^{0}$ , $π^{-} Σ^{+}$ , $π^{0} Σ^{0}$ , $π^{+} Σ^{-}$ , and $η Λ$ scattering processes. The blue solid lines denote the fit including a bare quark-model-like basis state, while the red dashed lines denote the fit without including a bare-baryon component. The peaks around 400 MeV are associated with the $D$ -wave $Λ (1520)$ state which is not considered in this work as described in the text.
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Figure 2
The pion mass dependence of the eigenstates obtained using the finite-volume Hamiltonian. In the upper plot, the broken lines denote noninteracting meson-baryon energies, while the solid lines denote the eigenenergies obtained from the finite-volume Hamiltonian matrix. In the lower plot, energy eigenstates based on the inclusion of a bare quark-model-like basis state are illustrated. The thick (red), dot-dashed (blue), and dotted (green) lines label the states composed with a significant contribution from the bare quark-model-like basis state, with red illustrating the largest bare state component. The negligible component of the bare basis state in the first state of the spectrum at light quark masses explains its absence in the lattice QCD spectrum excited with local three-quark operators. The lattice results are taken from the CSSM group [31, 38] in $2 + 1$ flavor QCD [99].
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Figure 3
The pion mass dependence of the Hamiltonian matrix eigenvector components for the first six states, under the assumption of no bare-baryon (left two columns) and including a bare-baryon basis (right two columns). The five circles in each diagram represent the five quark masses considered by the CSSM group [31, 38] in $2 + 1$ flavor QCD [99].
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Figure 4
Error estimation for the spectrum of odd-parity strange spin- $1 / 2$ baryons in HEFT for the CSSM lattice volume. The black solid lines represent the values with the optimal Hamiltonian parameters while the blue shaded regions illustrate the uncertainty in the HEFT results obtained through the allowed variation of Hamiltonian parameters as described in Sec. 4c.
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Figure 5
The energy eigenvalues calculated in HEFT in the scenario including a quark-model-like single-particle basis state (solid black lines) are compared with lattice QCD calculations from the BaSc collaboration [62, 63] in the $G_{1 u} (0)$ irreducible representation (data points) on a $L = 4.05 fm$ lattice. Dashed lines indicate the meson-baryon thresholds. The blue shaded regions illustrate the uncertainty in the HEFT predictions obtained through the allowed variation of Hamiltonian parameters as described in Sec. 4c.
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Physical Review D

covering particles, fields, gravitation, and cosmology

Structure of the $Λ (1670)$ resonance

Jiong-Jiong Liu, Zhan-Wei Liu, Kan Chen, Dan Guo, Derek B. Leinweber, Xiang Liu, and Anthony W. Thomas

Phys. Rev. D 109, 054025 – Published 18 March 2024

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Physical Review D

covering particles, fields, gravitation, and cosmology

Structure of the Λ(1670) resonance

Jiong-Jiong Liu, Zhan-Wei Liu, Kan Chen, Dan Guo, Derek B. Leinweber, Xiang Liu, and Anthony W. Thomas

Phys. Rev. D 109, 054025 – Published 18 March 2024

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Structure of the $Λ (1670)$ resonance