In a recent measurement LHCb reported pronounced structures in the $J/\psi J/\psi$ spectrum. One of the various possible explanations of those is that they emerge from non-perturbative interactions of vector charmonia. It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons, which hadronise into two pions at the longest distance. In this paper, we demonstrate that, given our current understanding of hadron-hadron interactions, the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di-$J/\psi$ system, and it is possible for two $J/\psi$ mesons to form a bound state. As a side result we find from an analysis of the data for the $\psi \left(2S\right)\to J/\psi \pi \pi$ transition including both $\pi \pi$ and $K\overline{K}$ final state interactions an improved value for the $\psi \left(2S\right)\to J/\psi$ transition chromo-electric polarisability: $\left|{\alpha }_{\psi \left(2S\right)J/\psi }\right|=(1.8\pm 0.1){\mathrm{GeV}}^{-3}$, where the uncertainty also includes the one induced by the final state interactions.

在最近的一次测量中，LHCb 报告了显着的结构$杰/\psi 杰/\psi$光谱。对这些的各种可能解释之一是它们来自矢量 charmonia 的非微扰相互作用。因此，重要的是要了解是否有可能通过交换胶子形成两个 charmonia 相互作用的束缚状态，胶子在最长距离处变成两个π介子。在这篇论文中，我们证明，鉴于我们目前对强子-强子相互作用的理解，相关轻介子（π介子和介子）的交换能够为二-强子提供相当大的吸引力。$杰/\psi$系统，并且有可能为两个$杰/\psi$介子形成束缚态。作为附带结果，我们从对数据的分析中发现$\psi \left(\mathrm{2个}\mathrm{小号}\right)\to 杰/\psi \pi \pi$过渡包括两者$\pi \pi$和$钾\overline{钾}$最终状态交互的改进值$\psi \left(\mathrm{2个}\mathrm{小号}\right)\to 杰/\psi$过渡色电极化率：$\left|{\alpha }_{\psi \left(\mathrm{2个}\mathrm{小号}\right)杰/\psi }\right|=(1.8\pm 0.1){\mathrm{GeV}}^{-\mathrm{3个}}$，其中不确定性还包括由最终状态相互作用引起的不确定性。