Doubly charged vector tetraquark $Z_{\mathrm{V}}^{++}=[cu][\overline{s}\overline{d}]$

Abstract

We explore properties of the doubly charged vector tetraquark $Z_{\mathrm{V}}^{++}=[cu][\overline{s}\overline{d}]$ built of four quarks of different flavors using the QCD sum rule methods. The mass and current coupling of $Z_{\mathrm{V}}^{++}$ are computed in the framework of the QCD two-point sum rule approach by taking into account quark, gluon and mixed vacuum condensates up to dimension $10$. The full width of this tetraquark is saturated by $S$-wave $Z_{\mathrm{V}}^{++}\to \ddot{I}{€}^{+}{D}_{s1}(2460{)}^{+},\ddot{I}{}^{+}{D}_{s0}^{\ast }(2317{)}^{+}$, and $P$-wave $Z_{\mathrm{V}}^{++}\to \ddot{I}{€}^{+}{D}_s^{+},K^{+}{D}^{+}$ decays. Strong couplings required to find partial widths of aforementioned decays are calculated in the context of the QCD light-cone sum rule method and a soft-meson approximation. Our predictions for the mass $m=(3515\pm 125)\mathrm{MeV}$ and full width $\hat{I}{“}_{\mathrm{full}}=156_{-30}^{+56}\mathrm{MeV}$ of $Z_{\mathrm{V}}^{++}$ are useful to search for this exotic meson in various processes. Recently, the LHCb collaboration discovered neutral states $X_{0(1)}(2900)$ as resonance-like peaks in $D^{-}{K}^{+}$ invariant mass distribution in the decay $B^{+}\to D^{+}{D}^{-}{K}^{+}$. We argue that mass distribution of $D^{+}{K}^{+}$ mesons in the same $B$ decay can be used to observe the doubly charged scalar $Z_{\mathrm{S}}^{++}$ and vector $Z_{\mathrm{V}}^{++}$ tetraquarks.

11 Pages, 2 Figures and 1 Table