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The low-lying $sQ\bar{q}\bar{q}$ $(q=u,\,d,\, Q=c,\,b)$ tetraquark stateswith $J^P=0^+$, $1^+$ and $2^+$, and in the isoscalar and isovector sectors,are systematically investigated in the framework of real- and complex-scalingrange of a chiral quark model, whose parameters have been fixed in advancedescribing hadron, hadron-hadron and multiquark phenomenology, and thus allresults presented here are pure predictions. Each tetraquark configuration,compatible with the quantum numbers studied, is taken into account; thisincludes meson-meson, diquark-antidiquark and K-type arrangements of quarkswith all possible color wave functions in four-body sector. Among the differentnumerical techniques to solve the Schr\"odinger-like 4-body bound stateequation, we use a variational method in which the trial wave function isexpanded in complex-range Gaussian basis functions, because its simplicity andflexibility. Several compact bound states and narrow resonances are found inboth charm-strange $cs\bar{q}\bar{q}$ and bottom-strange $bs\bar{q}\bar{q}$tetraquark sectors, most of them as a product of the strong coupling betweenthe different channels. The so-called $X_{0,1}(2900)$ signals, recently foundby the LHCb collaboration, are unstable in our formalism with severalcandidates in the single-channel computations.

The $\mathbf{sQ\bar{q}\bar{q}}$ $\mathbf{(q=u,\,d;\, Q=c,\,b)}$ tetraquarks in the chiral quark model