Unified description of the $Qs\bar{q}\bar{q}$ molecular bound states, molecular resonances and compact tetraquark states in the quark potential model

Abstract

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 Schrödinger equation, and use the complex scaling method to identify the resonances. With the notation $T_{Qs,I(J)}^{\text{Theo. }}(M)$, we find several near-threshold bound states and resonances, including $T_{cs,0(0)}^{Theo.}(2350)$, $T_{cs,0(0)}^{Theo.}(2906)$, $T_{bs,0(0)}^{Theo.}(5781)$, $T_{bs,0(1)}^{Theo.}(5840)$, and $T_{bs,0(0)}^{Theo.}(6240)$ which are close to the $D\bar{K}$, $D^{\ast }{\bar{K}}^{\ast }$, $\bar{B}\bar{K}$, ${\bar{B}}^{\ast }\bar{K}$ and ${\bar{B}}^{\ast }{\bar{K}}^{\ast }$ thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance $T_{cs,0(0)}^{Theo.}(2906)$ 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.

Comments: 9 pages, 4 figures, 3 tables. Version accepted by PRD