Charmed partner of the exotic $X(5568)$ state and its properties

Abstract

The mass, decay constant and width of a hypothetical charmed partner $X_c$ of the newly observed exotic $X_b(5568)$ state are calculated using a technique of QCD sum rule method. The $X_c=[su][\overline{c}\overline{d}]$ state with $J^{P}=0^{+}$ is described employing two types of the diquark-antidiquark interpolating currents. The evaluation of the mass $m_{X_c}$ and decay constant $f_{X_c}$ is carried out utilizing the two-point sum rule method by including vacuum condensates up to eight dimensions. The widths of the decay channels $X_c \to D_s^{-} \pi^{+}$ and $X_c \to D^{0} K^{0}$ are also found. To this end, the strong couplings $g_{X_{c}D_{s}\pi}$ and $g_{X_{c}D K}$ are computed by means of QCD sum rules on the light-cone and soft-meson approximation.