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The spectra of $bc\bar{b}\bar{c}$ tetraquark states from a diquark-antidiquark perspective

Zhen-Yang Wang, Jing-Juan Qi, Zhen-Hua Zhang, Xin-Heng Guo

TL;DR

This work investigates the spectra of fully heavy $bc\bar{b}\bar{c}$ tetraquarks within a diquark–antidiquark framework using the Bethe–Salpeter equation at leading order in $1/m_Q$. The kernel combines scalar confinement and one-gluon exchange, with diquark internal structure encoded by form factors and implemented under the covariant instantaneous approximation. Numerical solutions show all ground $S$-wave states have masses above the lowest heavy-meson pair thresholds, implying broad resonances that can decay via quark rearrangement. These results contribute to the understanding of fully heavy tetraquark dynamics and provide theoretical benchmarks for upcoming experimental searches at Belle-II and LHCb.

Abstract

Within the diquark-antidiquark framework, this study investigates the masses of ground-state tetraquarks composed of heavy charm ($c$) and bottom ($b$) quarks and antiquarks, using the Bethe-Salpeter formalism. We establish the Bethe-Salpeter equations for the fully heavy $bc\bar{b}\bar{c}$ tetraquarks to the leading order in $1/m_Q$ expansion. These equations are subsequently solved numerically under the covariant instantaneous approximation with kernels containing scalar confinement and one-gluon exchange terms. Our results show that the spectra of all possible $S$-wave tetraquark states are above the corresponding two lowest meson decay thresholds via the quark rearrangement. This implies that the ground $bc\bar{b}\bar{c}$ tetraquark states should be broad.

The spectra of $bc\bar{b}\bar{c}$ tetraquark states from a diquark-antidiquark perspective

TL;DR

This work investigates the spectra of fully heavy tetraquarks within a diquark–antidiquark framework using the Bethe–Salpeter equation at leading order in . The kernel combines scalar confinement and one-gluon exchange, with diquark internal structure encoded by form factors and implemented under the covariant instantaneous approximation. Numerical solutions show all ground -wave states have masses above the lowest heavy-meson pair thresholds, implying broad resonances that can decay via quark rearrangement. These results contribute to the understanding of fully heavy tetraquark dynamics and provide theoretical benchmarks for upcoming experimental searches at Belle-II and LHCb.

Abstract

Within the diquark-antidiquark framework, this study investigates the masses of ground-state tetraquarks composed of heavy charm () and bottom () quarks and antiquarks, using the Bethe-Salpeter formalism. We establish the Bethe-Salpeter equations for the fully heavy tetraquarks to the leading order in expansion. These equations are subsequently solved numerically under the covariant instantaneous approximation with kernels containing scalar confinement and one-gluon exchange terms. Our results show that the spectra of all possible -wave tetraquark states are above the corresponding two lowest meson decay thresholds via the quark rearrangement. This implies that the ground tetraquark states should be broad.

Paper Structure

This paper contains 9 sections, 38 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The BS equation for the $bc\bar{b}\bar{c}$ system
  3. The tetraquark composed of a scalar diquark and a scalar antidiquark
  4. The tetraquark composed of an axial-vector diquark and a scalar antidiquark
  5. The tetraquark composed of an axial-vector diquark and an axial-vector antidiquark
  6. The kernel for the BS equation
  7. Numerical results
  8. Summary and Discussion
  9. The symmetry properties of the BS wave functions

Figures (3)

  • Figure 1: The diquark-gluon-diquark vertex.
  • Figure 2: The mass spectra of (a) $J^{PC}=0^{++} {\vert}SS{\rangle}$, (b) $J^{PC}=1^{+-} {\vert}AS{\rangle}$, (c) $J^{PC}=1^{++} {\vert}AS{\rangle}$, (d) $J^{PC}=0^{++} {\vert}AA{\rangle}$, (e) $J^{PC}=1^{+-} {\vert}AA{\rangle}$, and (f) $J^{PC}=2^{++} {\vert}AA{\rangle}$ tetraquark states as functions of $\alpha_S$ for different $\beta$.
  • Figure 3: Numerical results of the scalar wave function for (a) $J^{PC}=0^{++} {\vert}SS{\rangle}$, (b) $J^{PC}=1^{+-} {\vert}AS{\rangle}$, (c) $J^{PC}=1^{++} {\vert}AS{\rangle}$, (d) $J^{PC}=0^{++} {\vert}AA{\rangle}$, (e) $J^{PC}=1^{+-} {\vert}AA{\rangle}$, and (f) $J^{PC}=2^{++} {\vert}AA{\rangle}$ tetraquark states with $\alpha=0.65$ and $\beta$=1.0.