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Meson-nucleus bound states with neural-network quantum states

Wei-Lin Wu1,*, Liang-Zhen Wen1,†, and Shi-Lin Zhu2,‡

  • *Contact author: wlwu@pku.edu.cn
  • †Contact author: wenlzh_hep-th@stu.pku.edu.cn
  • ‡Contact author: zhusl@pku.edu.cn
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Phys. Rev. D 114, 054060 – Published 30 September, 2026

DOI: https://doi.org/10.1103/3nrk-c5c7

Abstract

We present the first systematic calculations of ϕ-, ηc-, and J/ψ-nucleus ground states up to mass number A=12 based on the HAL QCD meson-nucleon potentials at near-physical point. The (A+1)-body Schrödinger equation is solved with a neural-network variational Monte Carlo framework, generalized to incorporate mesonic degrees of freedom. Benchmarking on light nuclei from H2 to C12 yields ground-state energies consistent with the experiment. Meson-nucleus bound states emerge at A≥2 for ϕ, A≥4 for J/ψ, and A≥6 for ηc. The ϕ-nucleus systems exhibit the strongest binding, with binding energies reaching tens of MeV. The J/ψ-nucleus and ηc-nucleus systems are weakly bound at the few-MeV and sub-MeV scale, respectively. The binding energy per nucleon deepens nearly linearly with A for charmonium systems, whereas the ϕ-nucleus system exhibits a nonmonotonic behavior peaking at He4—a distinctive hallmark of the short-range and strongly attractive ϕN interaction. The meson compresses the nucleon distribution relative to the parent nucleus, and evolves from a halo configuration to one embedded inside the nucleus with increasing A. Our results provide predictions for future experimental searches, and establish a quantitative bridge between lattice QCD meson-nucleon interactions and the emergent many-body phenomena in meson-nucleus bound states.

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Phys. Rev. D 114, 054060– Published 30 September, 2026
  • Received 11 June 2026
  • Accepted 18 September 2026
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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.

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