Fully-heavy tetraquark spectra and production at hadron colliders

Motivated by the observation of exotic structure around 6900MeV in $J/\psi$-pair mass spectrum using proton-proton collision data LHCb collaboration, we study spectra fully-heavy tetraquarks within Bethe-Salpeter equation and Regge trajectory relation. The $X(6900)$ may be explained as a radially excited state with quark content $cc\bar{c}\bar{c}$ spin-parity $0^{++}(3S)$ or $2^{++}(3S)$ an orbitally $2P$ state. New structures 6.0GeV, 6.5GeV, 7.1GeV are predicted together. Other $bb\bar{b}\bar{b}$ $bc\bar{b}\bar{c}$ which experimentally prominent discussed. On other hand, S-wave tetraquark productions at hadron colliders investigated their cross-sections obtained.