Tensor Resonance in $J\mathrm{/}\psi J\mathrm{/}\psi$ Scattering from Lattice QCD

The $S$-wave scattering amplitudes of $J\mathrm{/}\psi J\mathrm{/}\psi$ with quantum numbers $J^{PC}=0^{++}$ and $2^{++}$ are determined up to 6600,MeV using lattice QCD calculations at $m_{\pi }\approx 420$ and 250,MeV. The ${}^1{S}_0$ $J\mathrm{/}\psi J\mathrm{/}\psi$ system exhibits a near-threshold attractive interaction, resulting in a virtual bound state with a binding energy of approximately 30-40,MeV. In contrast, the ${}^5{S}_2$ $J\mathrm{/}\psi J\mathrm{/}\psi$ system exhibits a repulsive interaction near threshold. These behaviors are primarily dominated by the quark rearrangement effect. Most notably, a resonance is observed in the ${}^5{S}_2$ $J\mathrm{/}\psi J\mathrm{/}\psi$ channel, with a mass around 6540,MeV and a width of approximately 540,MeV. The extracted mass and width are consistent with the $X(6600)$ (or $X(6400)$) observed by the ATLAS and CMS collaborations, and show little dependence on the sea pion mass.