Axial-vector and pseudoscalar tetraquarks [ud][$\overline{c}\overline{s}$]

Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks X${}_{AV}$ and X${}_{PS}$ with content [ud][$\overline{c}\overline{s}$] are calculated by means of the QCD sum rule methods. Masses and current couplings of X${}_{AV}$ and X${}_{PS}$ are found using two-point sum rule computations performed by taking into account various vacuum condensates up to dimension 10. The full width of the axial-vector state X${}_{AV}$ is evaluated by including into analysis S-wave decay modes X${}_{AV}$ → D*(2010)${}^{-}$K${}^{+}$, ${\overline{D}}^{\ast }$(2007)${}^0$K${}^0$, D${}^{-}$K*(892)${}^{+}$, and ${\overline{D}}^0$K*(892)${}^0$. In the case of X${}_{PS}$, we consider S-wave decay X${}_{PS}$ → ${\overline{D}}_0^{\ast }$(2300)${}^0$K${}^0$, and P-wave processes X${}_{PS}$ → D${}^{-}$K*(892)${}^{+}$ and X${}_{PS}$ → ${\overline{D}}^0$K*(892)${}^0$. To determine partial widths of these decay modes, we employ the QCD light-cone sum rule method and soft-meson approximation, which are necessary to estimate strong couplings at tetraquark-meson-meson vertices X${}_{AV}$D${}^{-}$D*(2010)${}^{-}$K${}^{+}$, etc. Our predictions for the mass m${}_{AV}$=(2800 ± 75) MeV and width ${\Gamma }_{AV}$=(58 ± 10) MeV of the tetraquark X${}_{AV}$, as well as results m${}_{PS}$=(3000 ± 60) MeV and ${\Gamma }_{PS}$=(65 ± 12) MeV for the same parameters of X${}_{PS}$ may be useful in future experimental studies of multiquark hadrons.