Is the resonance ${X}_{0}\left(2900\right)$ a ground-state or radially excited scalar tetraquark $\left[ud\right]\left[\overline{c}\overline{s}\right]$?

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 $\left[ud\right]\left[\overline{c}\overline{s}\right]$ and spin-parities ${J}^{P}={0}^{+}$. Our aim is to reveal whether or not one of these states can be identified with the resonance ${X}_{0}\left(2900\right)$, 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 vacuum condensates up to dimension 15 in the analysis. For an axial-axial structure of ${X}_{0}^{\left(\prime \right)}$, we find partial widths of the decays ${X}_{0}^{\left(\prime \right)}\to {D}^{-}{K}^{+}$ and ${X}_{0}^{\left(\prime \right)}\to {D}^{0}{K}^{0}$, and estimate full widths of the states ${X}_{0}^{\left(\prime \right)}$. To this end, we calculate the strong couplings at the vertices ${X}_{0}^{\left(\prime \right)}DK$ in the framework of the light-cone sum rule method. We also use technical approaches of the soft-meson approximation necessary to analyze tetraquark-meson-meson vertices. We obtain $m=\left(2545±160\right)\text{}\text{}\mathrm{MeV}$ and ${m}^{\prime }=\left(3320±120\right)\text{}\text{}\mathrm{MeV}$ [${m}_{S}=\left(2663±110\right)\text{}\text{}\mathrm{MeV}$ and ${m}_{S}^{\prime }=\left(3325±85\right)\text{}\text{}\mathrm{MeV}$ 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 ${\Gamma }_{0}=\left(140±29\right)\text{}\text{}\mathrm{MeV}$ and ${\Gamma }_{0}^{\prime }=\left(110±25\right)\text{}\text{}\mathrm{MeV}$, which allow us to interpret that neither is the resonance ${X}_{0}\left(2900\right)$. At the same time, these predictions provide important information about the ground-state and radially excited diquark-antidiquark structures ${X}_{0}$ and ${X}_{0}^{\prime }$, which should be objects of future experimental and theoretical studies.