Singly heavy tetraquark resonant states with multiple strange quarks

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 Schr\"odinger 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 $D_s\eta ^\prime ,{D_{(s)}^*}\phi ,{D_s}^*K^*$ and $D_s^*\bar{K}^*$ (and their bottom counterparts), providing targets for future experimental searches.