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

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 $Z_{\mathrm{V}}^{++} \to \pi ^{+}D_{s1}(2460)^{+},\ \rho^{+}D_{s0}^{\ast }(2317)^{+}$, and $P$-wave $Z_{\mathrm{V}}^{++} \to \pi ^{+}D_{s}^{+},\ K^{+}D^{+}$ 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 $\Gamma _{\mathrm{full}}=156_{-30}^{+56}~\mathrm{MeV}$ 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.