Tri-meson state $\bar{\mathbf{B}}{\bar{\mathbf{B}}}^{\ast }{\bar{\mathbf{B}}}^{\ast }$

Abstract

We systematically explore the trimeson states $\bar{B}{\bar{B}}^{\ast }{\bar{B}}^{\ast }$ with various isospin-spin configurations in the quark model by solving exactly the six-body Schrödinger equations with the Gaussian expansion method. The configuration ${\left[[\bar{B}{\bar{B}}^{\ast }{]}_0^1{\bar{B}}^{\ast }\right]}_{\frac{1}{2}}^0$ is not only approximately 10.2 MeV lower than the threshold of its constituent particles but also about 0.2 MeV below that of the compact tetraquark state $[\bar{B}{\bar{B}}^{\ast }{]}_0^1$ and ${\bar{B}}^{\ast }$. This configuration manifests a loose two-body bound state composed of $[\bar{B}{\bar{B}}^{\ast }{]}_0^1$ and ${\bar{B}}^{\ast }$, with a size of around 4.75 fm. In contrast, the configurations ${\left[[\bar{B}{\bar{B}}^{\ast }{]}_1^1{\bar{B}}^{\ast }\right]}_{\frac{1}{2}}^0$, ${\left[\bar{B}[{\bar{B}}^{\ast }{\bar{B}}^{\ast }{]}_1^0\right]}_{\frac{1}{2}}^0$, and ${\left[[\bar{B}{\bar{B}}^{\ast }{]}_1^1{\bar{B}}^{\ast }\right]}_{\frac{1}{2}}^1$ exhibit binding energies of less than 1 MeV relative to their constituent particles, establishing a loose three-meson bound state. After coupling three configurations with $\frac{1}{2}{0}^{-}$, the trimeson state with $\frac{1}{2}{0}^{-}$ remains a loosely two-body bound state with a binding energy around 1.5 MeV and a huge size of 2.20 fm, in which the configuration ${\left[[\bar{B}{\bar{B}}^{\ast }{]}_0^1{\bar{B}}^{\ast }\right]}_{\frac{1}{2}}^0$ is dominant, contributing $80\%$ to the overall probability. Among the four bound configurations, the $\sigma$-meson exchange plays a decisive role. The meson pair $[\bar{B}{\bar{B}}^{\ast }{]}_0^1$, resembling the short-range strong correlated $p$-$n$ pair in nuclear physics, prevails over other types of meson pairs. The meson pair $[\bar{B}{\bar{B}}^{\ast }{]}_0^1$ not only contributes to the binding mechanisms but also influences the spatial structures of those stable trimeson configurations.

10 pages, 3 figures, 3 tables

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