Investigation of S-wave tetraquark bound and resonant states with all Jacobi coordinates

We systematically explore the $S$-wave tetraquark systems $Qs\bar{n}\bar{n}$, $QQ\bar{n}\bar{n}$, $QQ\bar{Q}\bar{Q}$, and $ss\bar{s}\bar{s}$ ($Q=c,b$; $n=u,d$) within the constituent quark potential model. We incorporate all K-type Jacobi coordinates in addition to the conventional H-type configurations, optimize the basis expansion via a stochastic parameter generation strategy, and apply the complex scaling method to identify bound and resonant states. Our calculations demonstrate that while conventional H-type configurations suffice for low-lying states such as the $T_{cc}(3875)^+$ molecular candidate, the inclusion of K-type configurations becomes important for extracting highly excited resonances, allowing higher-energy resonances absent in H-only calculations to be identified. Furthermore, we identify resonance candidates for the $T_{cs0}(2900)$, $X(6900)$, and $X(7200)$, whereas the absence of fully-strange compact poles below 2.6 GeV challenges the interpretation of $φ(2170)$ and $X(2370)$ as $S$-wave compact $s s \bar{s} \bar{s}$ tetraquarks.