Is the resonance $X_0(2900)$ a ground-state or radially excited scalar tetraquark $[ud][\overline{c}\overline{s}]$?

Abstract

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.

Comments: 13 Pages, 4 Figures and 2 Tables