We calculate the mass spectrum of the $Qs\bar q \bar q$ $(Q=c, b)$ tetraquark states with $J^P=(0,1,2)^+$ using the AL1 quark potential model, which successfully describes the conventional hadron spectrum. We employ the Gaussian expansion method to solve the four-body Schr\"odinger equation, and use the complex scaling method to identify the resonances. With the notation $T_{ Q s, I(J)}^{ \text { Theo. }}(M)$, we find several near-threshold bound states and resonances, including $T_{ cs,0(0)}^{ \mathrm{ Theo.}}(2350)$, $T_{ cs,0(0)}^{ \mathrm{ Theo.}}(2906)$, $T_{ bs,0(0)}^{ \mathrm{ Theo.}}(5781)$, $T_{ bs,0(1)}^{ \mathrm{ Theo.}}(5840)$, and $T_{ bs,0(0)}^{ \mathrm{ Theo.}}(6240)$ which are close to the $D\bar{ K}$, $D^*\bar{ K}^*$, $\bar{ B}\bar{ K}$, $\bar{ B}^*\bar{ K}$ and $\bar{ B}^*\bar{ K}^*$ thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance $T_{ cs,0(0)}^{ \mathrm{ Theo.}}(2906)$ has a mass of $2906$ MeV, a width of $20$ MeV, and quantum numbers $I(J^P)=0(0^+)$, which may serve as a good candidate for the experimental $T_{ cs0}(2900)$ state. We strongly urge the experimental search of the predicted states.
Categories: hep-ph hep-ex hep-lat nucl-th