We have systematically investigated the mass spectrum and rearrangement decay properties of the exotic tetraquark states with four different flavors using a color-magnetic interaction model. Their masses are estimated by assuming that the $X(4140)$ is a $cs\overline{c}\overline{s}$ tetraquark state and their decay widths are obtained by assuming that the Hamiltonian for decay is a constant. According to the adopted method, we find that the most stable states are probably the isoscalar $bs\overline{u}\overline{d}$ and $cs\overline{u}\overline{d}$ with $J^P=0^{+}$ and $1^{+}$. The width for most unstable tetraquarks is about tens of MeVs, but that for unstable $cu\overline{s}\overline{d}$ and $cs\overline{u}\overline{d}$ can be around 100 MeV. For the $X(5568)$, our method cannot give consistent mass and width if it is a $bu\overline{s}\overline{d}$ tetraquark state. For the $I(J^P)=0(0^{+}),0(1^{+})$ double-heavy $T_{bc}=bc\overline{u}\overline{d}$ states, their widths can be several MeVs.

• Received 18 January 2020
• Accepted 28 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.114017

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Published by the American Physical Society