Tri-meson state $\boldsymbol{\bar{B}\bar{B}^*\bar{B}^*}$

Abstract: We systematically explore the trimeson states $\bar{B}\bar{B}^\bar{B}^$ with various isospin-spin configurations in the quark model by solving exactly the six-body Schr\"{o}dinger equations with the Gaussian expansion method. The configuration $\left[[\bar{B} \bar{B}^]^1_0\bar{B}^\right]^0_{\frac{1}{2}}$ 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 $[\bar{B}\bar{B}^*]^1_0$ and $\bar{B}^*$. This configuration manifests a loose two-body bound state composed of $[\bar{B}\bar{B}^*]^1_0$ and $\bar{B}^* $, with a size of around 4.75 fm. In contrast, the configurations $\left[[\bar{B}\bar{B}^]^1_1\bar{B}^\right]^0_{\frac{1}{2}}$, $\left[\bar{B}[\bar{B}^\bar{B}^]^0_1\right]^0_{\frac{1}{2}}$, and $\left[[\bar{B}\bar{B}^]^1_1\bar{B}^\right]^1_{\frac{1}{2}}$ 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 $\left[[\bar{B}\bar{B}^]^1_0\bar{B}^\right]^0_{\frac{1}{2}}$ is dominant, contributing $80\%$ to the overall probability. Among the four bound configurations, the $\sigma$-meson exchange plays a decisive role. The meson pair $[\bar{B}\bar{B}^*]^1_0$, resembling the short-range strong correlated $p$-$n$ pair in nuclear physics, prevails over other types of meson pairs. The meson pair $[\bar{B}\bar{B}^*]^1_0$ not only contributes to the binding mechanisms but also influences the spatial structures of those stable trimeson configurations.