Resonance $X(3960)$ as a hidden charm-strange scalar tetraquark

Abstract: We investigate features of the hidden charm-strange scalar tetraquark $c \overline{c}s\overline{s}$ by calculating its spectral parameters and width, and we compare the obtained results with the mass and width of the resonance $ X(3960)$ discovered recently in the LHCb experiment. We model the tetraquark as a diquark-antidiquark state $X=[cs][\overline{c}\overline{s}]$ with spin-parities $J^{\mathrm{PC}}=0^{++}$. The mass and current coupling of $X$ are calculated using the QCD two-point sum rules by taking into account various vacuum condensates up to dimension $10$. The width of the tetraquark $X$ is estimated via the decay channels $X \to D_{s}^{+}D_{s}^{-}$ and $X \to \eta_{c} \eta^{(\prime)}$. The partial widths of these processes are expressed in terms of couplings $G$, $g_1$ and $g_2$ which describe the strong interactions of particles at the vertices $XD_{s}^{+}D_{s}^{-}$, $ X\eta_{c}\eta^{\prime}$ and $X\eta_{c}\eta$, respectively. Numerical values of $G$, $g_1$ and $g_2$ are evaluated by employing the three-point sum rule method. Comparing the results $m=(3976 \pm 85)~\mathrm{MeV}$ and $\Gamma_{ \mathrm{X}}=(42.2 \pm 12.0)~\mathrm{MeV}$ obtained for parameters of the tetraquark $X$ and experimental data of the LHCb Collaboration, we conclude that the resonance $X(3960)$ can be considered as a candidate to a scalar diquark-antidiquark state.