The Doubly-heavy Tetraquarks ($qq'\bar{Q}\bar{Q'}$) in a Constituent Quark Model with a Complete Set of Harmonic Oscillator Bases

We have improved our previous variational method based constituent quark model by introducing a complete set of 3-dimensional harmonic oscillator bases as the spatial part of the total wave function. To assess the validity of our approach, we compared the binding energy, thus calculated with the exact value for the hydrogen model. After fitting to the masses of the ground state hadrons, we apply our new method to analyze the doubly-heavy tetraquark states $qq'\bar{Q}\bar{Q'}$ and compared the result for the binding energies with that from other works. We also calculated the ground state masses of $T_{sc} (ud\bar{s}\bar{c})$ and $T_{sb} (ud\bar{s}\bar{b})$ with $(I,S) = (0,1), (0,2)$. We found that $T_{bb} (ud\bar{b}\bar{b})$ and $us\bar{b}\bar{b}$, both with $(I,S) = (0,1)$, are stable against the two lowest threshold meson states with binding energies $-145$ MeV and $-42$ MeV, respectively. We further found that $T_{cb} (ud\bar{c}\bar{b})$ is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.