Inspired by the observation of the $X(6900)$ by LHCb and the $X(6600)$ (with mass $6552\pm 10$ $\pm 12$ MeV) recently by CMS and ATLAS experiments of the LHC in the di-$J/\Psi $ invariant mass spectrum, we systemically study masses of all ground-state configurations of the hidden heavy-flavor tetraquarks $q_{ 1}Q_{ 2}\bar{ q}_{ 3}\bar{ Q}_{ 4}$ and $Q_{ 1}Q_{ 2}\bar{ Q}_{ 3}\bar{ Q}_{ 4}$ ($Q=c,b$;$q=u,d,s$) contaning two and four heavy quarks in the MIT bag model with chromomagnetic interaction and enhanced binding energy. Considering color-spin mixing due to chromomagnetic interaction, our mass computation indicates that the observed $X(6600)$ is likely to be the $0^{ ++}$ ground states of hidden-charm tetraquark $cc\bar{ c}\bar{ c}$ with computed masses $6572$ MeV, which has a $0^{ ++}$ color partner around $6469$ MeV. The fully bottom system of tetraquark $bb\bar{ b}\bar{ b}$ has masses of 19685 MeV and 19717 MeV for the the $0^{ ++}$ ground states. Further computation is given to the tetraquark systems $sc\bar{ s}\bar{ c}$, $sb\bar{ s}\bar{ b}$, $cb\bar{ c}\bar{ b}$, $nc\bar{ n}\bar{ c}$ and $nb\bar{ n}\bar{ b}$, suggesting that the $Z_{ c}(4200)$ is the tetraquark $nc\bar{ n}\bar{ c}$ with $J^{ PC}=1^{ +-}$. All of these tetraquarks are above their lowest thresholds of two mesons and unstable against the strong decays.
Categories: hep-ph