Singly heavy tetraquark resonant states with multiple strange quarks

TL;DR

The paper addresses the existence and internal structure of S-wave singly heavy tetraquarks containing multiple strange quarks by solving the four-body problem with the AL1 constituent-quark potential using the Gaussian Expansion Method and identifying resonances through the Complex Scaling Method. It finds no bound states below the lowest meson thresholds but reveals several compact resonances with $J^P = 0^+$ and $2^+$ in both charm and bottom sectors, with pole positions near $M \sim 3.7$–$3.9$ GeV (charm) and $M \sim 7.0$–$7.2$ GeV (bottom) and widths ranging from a few to a few tens of MeV. These resonances decay into channels such as $D_s\eta^\prime$, $D_{(s)}^*\phi$, $D_s^*K^*$ and their bottom counterparts, providing concrete targets for experimental searches at LHCb and Belle II. The results illustrate how strangeness and heavy-quark flavor influence the spectrum and offer a coherent framework for interpreting open-flavor exotic candidates within a unified four-quark treatment.

Abstract

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, $Qs\bar{s}\bar{s}$, $Qn\bar{s}\bar{s}$ and $Qs\bar{s}\bar{n}\left( Q=c,b,n=u,d \right) $, within the constituent quark potential model. We solve the four-body Schrödinger equation using the Gaussian expansion method (GEM) and identify resonances via the complex scaling method (CSM). There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with $J^P=0^+,2^+$ in $Qs\bar{s}\bar{s}$, and $J^P=2^+$ in $Qn\bar{s}\bar{s}$ and $Qs\bar{s}\bar{n}$. The pole positions are mainly distributed around $7.0-7.2$ GeV (bottom) and $3.7-3.9$ GeV (charm), with widths from a few to several tens of MeV. These resonances decay into $D_sη^\prime ,{D_{(s)}^*}φ,{D_s}^*K^*$ and $D_s^*\bar{K}^*$ (and their bottom counterparts), providing targets for future experimental searches.

Figures (4)

• Figure 1: Two structures of the tetraquark system. (a) diquark-antidiquark structure. (b) dimeson structure.
• Figure 2: The complex energy eigenvalues of the $Qs \bar{s} \bar{s}$ states in the AL1 potential with varying $\theta$ in the CSM. The dashed lines represent the continuum lines rotating along $\mathrm{Arg}(E)=-2\theta$. The resonant states do not shift as $\theta$ changes and are marked out by the black circles.
• Figure 3: The complex energy eigenvalues of the $Qn \bar{s} \bar{s}$ states in the AL1 potential with varying $\theta$ in the CSM. The dashed lines represent the continuum lines rotating along $\mathrm{Arg}(E)=-2\theta$. The resonant states do not shift as $\theta$ changes and are marked out by the black circles.
• Figure 4: The complex energy eigenvalues of the $Qs \bar{s} \bar{n}$ states in the AL1 potential with varying $\theta$ in the CSM. The dashed lines represent the continuum lines rotating along $\mathrm{Arg}(E)=-2\theta$. The resonant states do not shift as $\theta$ changes and are marked out by the black circles.