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

Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks ${X}_{\text{AV}}$ and ${X}_{\text{PS}}$ with content $\left[ud\right]\left[\overline{c}\overline{s}\right]$ are calculated by means of the QCD sum rule methods. Masses and current couplings of ${X}_{\text{AV}}$ and ${X}_{\text{PS}}$ 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 ${X}_{\text{AV}}$ is evaluated by including into analysis S-wave decay modes ${X}_{\text{AV}}\to {D}^{\ast }{\left(2010\right)}^{-}{K}^{+}$ , ${\overline{D}}^{\ast }{\left(2007\right)}^{0}{K}^{0}$ , ${D}^{-}{K}^{\ast }{\left(892\right)}^{+}$ , and ${\overline{D}}^{0}{K}^{\ast }{\left(892\right)}^{0}$ . In the case of ${X}_{\text{PS}}$ , we consider S-wave decay ${X}_{\text{PS}}\to {\overline{D}}_{0}^{\ast }{\left(2300\right)}^{0}{K}^{0}$ , and P-wave processes ${X}_{\text{PS}}\to {D}^{-}{K}^{\ast }{\left(892\right)}^{+}$ and ${X}_{\text{PS}}\to {\overline{D}}^{0}{K}^{\ast }{\left(892\right)}^{0}$ . 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 ${X}_{\text{AV}}{D}^{-}{D}^{\ast }{\left(2010\right)}^{-}{K}^{+}$ , etc. Our predictions for the mass ${m}_{\text{AV}}=\left(2800±75\right)\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ and width ${\Gamma }_{\text{AV}}=\left(58±10\right)\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ of the tetraquark ${X}_{\text{AV}}$ , as well as results ${m}_{\text{PS}}=\left(3000±60\right)\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ and ${\Gamma }_{\text{PS}}=\left(65±12\right)\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ for the same parameters of ${X}_{\text{PS}}$ may be useful in future experimental studies of multiquark hadrons.