Hidden heavy flavor tetraquarks in the Born-Oppenheimer approximation

The Born-Oppenheimer approximation is one of the very successful tools for solving the hydrogen atom problem. The experimental discovery of hidden heavy flavor tetraquarks, $Q\bar{Q}q \bar{q}$ ($Q=c,b$ and $q=u,d,s$), provides great possibilities for the hydrogen-bond-like structure of the Quantum Chromodynamics version. In this work, considering that the colors of $Q\bar{Q}$ and $q\bar{q}$ are both $8$, the tetraquark $Q\bar{Q}q \bar{q}$ system is formed by color coupling $8\otimes8 \rightarrow 1$. In order to study the mass splitting caused by the color-spin hyperfine interaction, the color-spin basis vectors of the $S$-wave tetraquark states are appropriately constructed. Then we use the Born-Oppenheimer approximation to calculate the mass spectra of the $S$-wave hidden heavy flavor tetraquark states. The results show that some of the hidden heavy flavor exotic hadrons discovered experimentally can be well explained as this type of hydrogen-bond-like tetraquark structure. In addition, some candidates for tetraquark bound states are predicted and may be compact tetraquark states.