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Hydrogenlike structures in the strong interaction

College of Physics, Chengdu University of Technology, Chengdu 610059, China

^*Contact author: guot17@tsinghua.org.cn

Phys. Rev. D 112, 054021 – Published 12 September, 2025

DOI: https://doi.org/10.1103/77hs-2gy4

Abstract

Heavy flavor hadrons, especially doubly heavy baryons and doubly heavy tetraquarks, have always received extensive attention in theoretical and experimental research. Given the separation of quark masses $m_{Q} ≫ m_{q}$ ( $Q = c$ , $b$ and $q = u$ , $d$ , $s$ ), this type of heavy flavor hadrons can be well regarded as hydrogenlike structures in the strong interaction. In the theoretical framework of Born-Oppenheimer approximation, we derive the Schrödinger equation for the motion of light quarks in the effective potential field of heavy quarks. Taking proper account of the color-spin hyperfine interaction, we carry out a systematic study on the mass spectra of $S$ -wave doubly heavy baryons and doubly heavy tetraquarks. The model parameters required for the calculation are obtained by fitting conventional hadrons. The investigation on the doubly heavy baryon systems indicates the reliability of our theoretical approach. Our calculation results show that the experimentally discovered $T_{c c}^{+}$ is most likely a compact tetraquark $| (c c)_{0}^{6} (\bar{u} \bar{d})_{1}^{\bar{6}} ⟩$ state with quantum numbers $(I, J^{P}) = (0, 1^{+})$ . Furthermore, for different quantum number assignments, some stable tetraquark states are found and may be very narrow peaks. The predictions for other heavy flavor hadrons are expected to be confirmed in new theories and future experiments.

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Phys. Rev. D 112, 054021– Published 12 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 23 June 2025
Accepted 26 August 2025

DOI: https://doi.org/10.1103/77hs-2gy4

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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Hydrogenlike structures in the strong interaction

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