The T_bc tetraquarks near the BD̅ threshold

Abstract

We study the doubly heavy open-flavor tetraquarks T_bc⁽⁰⁾ (J^P=0⁺) and T_bc⁽¹⁾ (J^P=1⁺) in the dynamical diquark model, treating them as heavy antidiquark--light diquark systems interacting through the lattice-QCD Σ_g⁺(1S) Born--Oppenheimer potential. Solving the radial Schrödinger equation gives M(T_bc⁽⁰⁾)=7.143--$7.158$ GeV and M(T_bc⁽¹⁾)=7.217--$7.222$ GeV, with hyperfine splittings Δ_HF≃59--$79$ MeV. The splitting is driven mainly by the mass difference between symmetric and antisymmetric heavy-antidiquark configurations, while the chromomagnetic contribution satisfies ∂Δ_HF/∂κ_b̅c̅=2, as required by heavy-antidiquark spin algebra. The mean separation, ⟨ r⟩≃0.45--$0.46$ fm, and inverse radius, ⟨1/r⟩⁻¹≃0.33--$0.34$ fm, show weak parameter dependence and support a compact diquark--antidiquark picture. The scalar mass lies essentially at the BD̅ threshold, allowing either a weakly decaying bound state or a narrow near-threshold structure. The axial-vector state lies $23−−28$ MeV above B^*D̅ and about $70$ MeV below BD̅^*, making it a natural S-wave resonance candidate with a line shape sensitive to the nearby B^*D̅ threshold. Parametric uncertainties are dominated by the light-diquark mass and largely cancel in mass differences. We also complete the Σ_g⁺(1S) multiplet: its four isovector members follow from the isoscalar states by a rigid shift 2κ_ud≈206 MeV and lie above all B^(*)D̅^(*) thresholds. Finally, the neglected 6̅⊗6 configuration is estimated to lie $0.1−−0.3$ GeV higher and to affect the spectrum only at second order.

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BibTeX RIS

BibTeX

@misc{mutuk2026tetraquarks,
  title = {{The $T_bc$ tetraquarks near the $B\barD$ threshold}},
  author = {Halil Mutuk},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.05150},
  eprint = {2605.05150},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.05150},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - The T_bc tetraquarks near the BD̅ threshold
AU  - Halil Mutuk
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2605.05150
UR  - https://arxiv.org/abs/2605.05150
AB  - We study the doubly heavy open-flavor tetraquarks T_bc^(0) (J^P=0^+) and T_bc^(1) (J^P=1^+) in the dynamical diquark model, treating them as heavy antidiquark--light diquark systems interacting through the lattice-QCD Σ_g^+(1S) Born--Oppenheimer potential. Solving the radial Schrödinger equation gives M(T_bc^(0))=7.143--$7.158$ GeV and M(T_bc^(1))=7.217--$7.222$ GeV, with hyperfine splittings Δ_HF≃59--$79$ MeV. The splitting is driven mainly by the mass difference between symmetric and antisymmetric heavy-antidiquark configurations, while the chromomagnetic contribution satisfies ∂Δ_HF/∂κ_b̅c̅=2, as required by heavy-antidiquark spin algebra. The mean separation, ⟨ r⟩≃0.45--$0.46$ fm, and inverse radius, ⟨1/r⟩^−1≃0.33--$0.34$ fm, show weak parameter dependence and support a compact diquark--antidiquark picture. The scalar mass lies essentially at the BD̅ threshold, allowing either a weakly decaying bound state or a narrow near-threshold structure. The axial-vector state lies $23−−28$ MeV above B^*D̅ and about $70$ MeV below BD̅^*, making it a natural S-wave resonance candidate with a line shape sensitive to the nearby B^*D̅ threshold. Parametric uncertainties are dominated by the light-diquark mass and largely cancel in mass differences. We also complete the Σ_g^+(1S) multiplet: its four isovector members follow from the isoscalar states by a rigid shift 2κ_ud≈206 MeV and lie above all B^(*)D̅^(*) thresholds. Finally, the neglected 6̅⊗6 configuration is estimated to lie $0.1−−0.3$ GeV higher and to affect the spectrum only at second order.
ER  -

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