We investigate properties of the ground-state and first radially excited four-quark mesons $X_0$ and $X_0^{ \prime}$ with a diquark-antidiquark structure $[ud][\overline{ c}\overline{ s}]$ and spin-parities $J^{ \mathrm{ P} }=0^{ +}$. Our aim is to reveal whether or not one of these states can be identified with the resonance $X_0(2900)$, recently discovered by the LHCb collaboration. We model $X_0$ and $X_0^{ \prime}$ as tetraquarks composed of either axial-vector or scalar diquark and antidiquark pairs. Their spectroscopic parameters are computed by employing the QCD two-point sum rule method and including into analysis vacuum condensates up to dimension $ 15$. For an axial-axial structure of $X_0^{ (\prime)}$, we find partial widths of the decays $X_0^{ (\prime)} \to D^{ -}K^{ +}$ and $X_0^{ (\prime)} \to D^{ 0}K^{ 0}$, and estimate full widths of the states $X_0^{ (\prime)}$. To this end, we calculate the strong couplings at the vertices $ X_0^{ (\prime)}DK $ in the framework of the light-cone sum rule method. We use also technical approaches of the soft-meson approximation necessary to analyze tetraquark-meson-meson vertices. Obtained results $m=(2545 \pm 160)~ \mathrm{ MeV}$ and $m^{ \prime}=(3320 \pm 120)~\mathrm{ MeV}$ [$m_{ \mathrm{ S} }=(2663 \pm 110)~\mathrm{ MeV}$ and $m_{ \mathrm{ S}}^{ \prime}=(3325 \pm 85)~ \mathrm{ MeV}$ for a scalar-scalar current] for the masses of the particles $ X_0$ and $X_0^{ \prime}$, as well as estimates for their full widths $ \Gamma_{ 0}=(140 \pm 29)~\mathrm{ MeV}$ and $\Gamma_{ 0}^{ \prime}=(110 \pm 25)~ \mathrm{ MeV}$ allow us to interpret none of them as the resonance $X_0(2900)$ . At the same time, these predictions provide important information about ground-state and radially excited diquark-antidiquark structures $X_0$ and $ X_0^{ \prime}$, which should be objects of future experimental and theoretical studies.
Categories: hep-ph hep-ex hep-lat