\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
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.
\end{document}