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

Abstract

Spectroscopic parameters and widths of the fully open-flavor axial-vector and pseudoscalar tetraquarks $X_{\mathrm{AV}}$ and $X_{\mathrm{PS}}$ with content $[ud][\overline{c}\overline{s}]$ are calculated by means of the QCD sum rule methods. Masses and current couplings of $X_{\mathrm{AV}}$ and $X_{\mathrm{PS}}$ 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 $X_{\mathrm{AV}}$ is evaluated by including into analysis $S$-wave decay modes $X_{\mathrm{AV}}\to D^{\ast }(2010{)}^{-}{K}^{+}$, ${\overline{D}}^{\ast }(2007{)}^0{K}^0$, $D^{-}{K}^{\ast }(892{)}^{+}$, and ${\overline{D}}^0{K}^{\ast }(892{)}^0$. In the case of $X_{\mathrm{PS}}$, we consider $S$-wave decay $X_{\mathrm{PS}}\to {\overline{D}}_0^{\ast }(2300{)}^0{K}^0$, and $P$-wave processes $X_{\mathrm{PS}}\to D^{-}{K}^{\ast }(892{)}^{+}$ and $X_{\mathrm{PS}}\to {\overline{D}}^0{K}^{\ast }(892{)}^0$. 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 $X_{\mathrm{AV}}{D}^{-}{D}^{\ast }(2010{)}^{-}{K}^{+}$, etc. Our predictions for the mass $m_{\mathrm{AV}}=(2800\pm 75)\mathrm{MeV}$ and width $\hat{I}{“}_{\mathrm{AV}}=(58\pm 10)\mathrm{MeV}$ of the tetraquark $X_{\mathrm{AV}}$, as well as results $m_{\mathrm{PS}}=(3000\pm 60)\mathrm{MeV}$ and $\hat{I}{“}_{\mathrm{PS}}=(65\pm 12)\mathrm{MeV}$ for the same parameters of $X_{\mathrm{PS}}$ may be useful in future experimental studies of multiquark hadrons.

14 Pages, 4 Figures and 2 Tables