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ϕNN, J/ψNN, ηcNN systems based on HAL QCD interactions

Liang-Zhen Wen1, Yao Ma2,*, Lu Meng3,†, and Shi-Lin Zhu2,‡

  • *Contact author: yaoma@pku.edu.cn
  • †Contact author: lu.meng@rub.de
  • ‡Contact author: zhusl@pku.edu.cn
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Phys. Rev. D 111, 114004 – Published 5 June, 2025Erratum Phys. Rev. D 112, 039901 (2025)

DOI: https://doi.org/10.1103/mvqk-n377

Abstract

We investigate the existence of bound states and resonances in the ϕNN,J/ψNN,ηcNN systems using HAL QCD interactions for ϕN,J/ψN, and ηcN. We employ the Gaussian expansion method to solve the complex-scaled Schrödinger equation and find no resonances or bound states in the J/ψNN and ηcNN systems. We estimate the interaction between charmonium and nuclei, concluding that the J/ψ or ηc is likely to bind with H3, He3, He4, and heavier nuclei. For the ϕNN system, the lattice QCD ϕN(S21/2) interaction is absent. We combine the ϕp correlation function analysis and HAL QCD results in model A. We assume the spin-spin interactions for J/ψN and ϕN systems are inversely proportional to their masses in model B. Model A predicts a stronger ϕN(S21/2) interaction and permits a two-body bound state, whereas model B suggests the interaction is attractive but too weak to form a bound state. Both models predict bound states for the I(JP)=0(0−) and 0(1−) ϕNN systems. In model A, these states are deeply bound with binding energies exceeding 15 MeV and remain existent when considering parameter uncertainties. In contrast, these states are very loosely bound in model B, with binding energies below 1 MeV and an existent probability of about 60% when parameter uncertainties are considered. In both models, there exist very loosely bound I(JP)=0(2−) three-body states which resemble a ϕ-d atom with the ϕ meson surrounding the deuteron, but their existence is sensitive to parameter uncertainties. No bound states or resonances are found in the isovector I(JP)=1(1−) ϕNN system.

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Erratum

Erratum: ϕNN, J/ψNN, ηcNN systems based on HAL QCD interactions [Phys. Rev. D 111, 114004 (2025)]

Liang-Zhen Wen, Yao Ma, Lu Meng, and Shi-Lin Zhu
Phys. Rev. D 112, 039901 (2025)

Article Text

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Phys. Rev. D 111, 114004– Published 5 June, 2025
  • Received 18 March 2025
  • Accepted 19 May 2025
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