Resonance $X(6600)$

The resonance $X(6600)$ is explored as the all-charm tetraquark structure with spin-parities $J^{\mathrm{PC}}=2^{++}$. It is considered in the diquark-antidiquark picture and modeled as a tensor state $X$ composed of the axial-vector diquark $cC\gamma_{\mu}c$ and antidiquark $\overline{c}$ with $C$ being the charge conjugation matrix. The mass and decay width of $X$ are evaluated in the framework of QCD sum rule (SR) methods. The two-point SR approach is applied to find its spectroscopic parameters, while three-point SRs used to calculate partial widths of different decay channels of $X$. We study its leading decays $X \to J/\psi J/\psi$, $X \to \eta_{c}\eta_{c}$ and $\chi _{c1}(1P)\eta _{c}$ in which all four $c$-quarks constitute final-state mesons. We consider also the subleading channels $X\to D_{(s)}^{(\ast )+}D_{(s)}^{(\ast )-}$ and $$ generated by annihilation of $\overline{c}c$ quarks in the tetraquark. Comparison of the mass $m=(6609 \pm 50)~ \mathrm{MeV}$ and width $\Gamma[X]=(165 \pm 23)~ \mathrm{MeV}$ of the tensor diquark-antidiquark state $X$ with experimental data allows us to interpret it as an essential component of the resonance $X(6600)$. We also provide a lower limit for the mass of the first radial excitation of $X$.