Resonance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3960</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> 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 $X\ensuremath{\rightarrow}{D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$ and $X\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}{\ensuremath{\eta}}^{(\ensuremath{'})}$. 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 $X{D}_{s}^{+}{D}_{s}^{\ensuremath{-}}$, $X{\ensuremath{\eta}}_{c}{\ensuremath{\eta}}^{\ensuremath{'}}$, and $X{\ensuremath{\eta}}_{c}\ensuremath{\eta}$, respectively. Numerical values of $G$, ${g}_{1}$, and ${g}_{2}$ are evaluated by employing the three-point sum rule method. Comparing the results $m=(3976\ifmmode\pm\else\textpm\fi{}85)\text{ }\text{ }\mathrm{MeV}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{X}}=(42.2\ifmmode\pm\else\textpm\fi{}12.0)\text{ }\text{ }\mathrm{MeV}$ 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.

Topics & Concepts