Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

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In this work, we calculate the higher mass spectra for the $2S$- and $1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie in the mass range of $\ensuremath{\sim}(6.9,7.1)/(19.7,19.9)\text{ }\mathrm{GeV}$, apart from the highest ${0}^{++}$ state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)/{T}_{(bb\overline{b}\overline{b}){0}^{++}}(19976)$. Most of the $2S$-wave states highly overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave fully-charmed/bottom tetraquark states are predicted to be in the range of $\ensuremath{\sim}(6.7,7.2)/(19.5,20.0)\text{ }\text{ }\mathrm{GeV}$. The mass range for the $D$-wave tetraquark states cover most of the mass range of the $P$-wave states and the whole mass range of the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb in the di-$J/\ensuremath{\psi}$ invariant mass spectrum may be caused by the $1P$-, or $2S$-, or $1D$-wave ${T}_{(cc\overline{c}\overline{c})}$ states. The vague structure $X(7200)$ may be caused by the highest $2S$-wave state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)$, two low-lying $3S$-wave states ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7240)$ and ${T}_{(cc\overline{c}\overline{c}){2}^{++}}(7248)$, and/or the high-lying $1D$-wave states with masses around 7.2 GeV and ${J}^{PC}={0}^{++},{1}^{++},{2}^{++},{3}^{++}$, or ${4}^{++}$. While it is apparent that the potential quark model calculations predict more states than the structures observed in the di-$J/\ensuremath{\psi}$ invariant mass spectrum, our calculations will help further understanding of the properties of these fully-heavy tetraquark states in their strong and magnetic interactions with open channels based on explicit quark model wave functions.