Tensor molecule $J/\psi J/\psi$: A candidate to the resonance $X(6200) $

The hadronic tensor molecule $\mathcal{M}=J/\psi J/\psi$ is investigated in the framework of QCD sum rule method. We evaluate its mass and current coupling using the two-point SR approach. Our result $m=(6290 \pm 50)~ \mathrm{MeV}$ for the mass of $\mathcal{M}$ indicates that it can decay to a pair of mesons $J/\psi J/\psi$. Apart from this dominant channel there are subdominant modes of the molecule $\mathcal{M}$ generated due to annihilation of constituent $\overline{c}c$ quarks to pairs of light quarks $\overline{q}q$ and $\overline{s}s$. This mechanism launches processes $\mathcal{M} \to D_{(s)}^{(\ast )+}D_{(s)}^{(\ast )-}$, $DD_{1}(2420)$, $D_sD_{s1}(2460)$ and $D_{(s)}^{(\ast )0}\overline{D}_{(s)}^{(\ast )0}$. The decays of $\mathcal{M}$ are explored by applying technical tools of the three-point sum rule approach which is necessary to estimate strong couplings at $\mathcal{M}$-meson-meson vertices. Comparing the mass $m$ of the molecule $\mathcal{M}$ and its decay width $\Gamma[\mathcal{M}]=(149 \pm 21)~ \mathrm{MeV}$ with available experimental data, we discuss the molecule $\mathcal{M}$ as a possible candidate to the tensor resonance $X(6200)$.