$T_{c\bar{s}0}^a(2900)$, $T_{cs0}^{\ast }(2870{)}^0$, and other singly-heavy tetraquark states

We systematically study the mass spectra of $S$-wave singly-heavy tetraquark states $Qq\bar{q}\bar{q}$ ($Q=c,b$; $q=u,d,s$) in a mass splitting model. We adopt the assumption that the $X(4140)$ is the lowest $J^{PC}=1^{++}$ $cs\bar{c}\bar{s}$ tetraquark and use this state as a reference to determine the mass splittings. According to the obtained results, we also estimate the rearrangement decay widths of the tetraquarks within a simple scheme. We find that the recently observed states $T_{c\bar{s}0}^a(2900{)}^{++\mathrm{/}0}$ and $T_{cs0}^{\ast }(2870{)}^0$ by the LHCb Collaboration can be consistently interpreted as the second highest $I(J^P)=1(0^{+})$ $cn\bar{s}\bar{n}$ ($n=u,d$) and the higher $I(J^P)=0(0^{+})$ $cs\bar{n}\bar{n}$ tetraquark states, respectively. We predict several narrow tetraquark candidates: the lowest $cn\bar{s}\bar{n}$ and $cs\bar{n}\bar{n}$ with $I(J^P)=0(0^{+})$ and $0(1^{+})$, and their bottom counterparts. The obtained information from mass spectrum and rearrangement decay properties will help search for the new singly-heavy tetraquark states.