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Fully-heavy tetraquark states, i.e. $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$,$bb\bar{c}\bar{c}$ ($cc\bar{b}\bar{b}$), $cb\bar{c}\bar{c}$,$cb\bar{b}\bar{b}$, and $cb\bar{c}\bar{b}$, are systematically investigated bymeans of a non-relativistic quark model based on lattice-QCD studies of thetwo-body $Q\bar{Q}$ interaction, which exhibits a spin-independent Cornellpotential along with a spin-spin term. The four-body problem is solved usingthe Gaussian expansion method; additionally, the so-called complex scalingtechnique is employed so that bound, resonance, and scattering states can betreated on the same footing. Moreover, a complete set of four-bodyconfigurations, including meson-meson, diquark-antidiquark, and K-typeconfigurations, as well as their couplings, are considered for spin-parityquantum numbers $J^{P(C)}=0^{+(+)}$, $1^{+(\pm)}$, and $2^{+(+)}$ in the$S$-wave channel. Several narrow resonances, with two-meson strong decay widthsless than 30 MeV, are found in all of the tetraquark systems studied.Particularly, the fully-charm resonances recently reported by the LHCbCollaboration, at the energy range between 6.2 and 7.2 GeV in the di-$J/\psi$invariant spectrum, can be well identified in our calculation. Focusing on thefully-bottom tetraquark spectrum, resonances with masses between 18.9 and 19.6GeV are found. For the remaining charm-bottom cases, the masses are obtainedwithin a energy region from 9.8 GeV to 16.4 GeV. All these predicted resonancescan be further examined in future experiments.

Exotic resonances of fully-heavy tetraquarks in a lattice-QCD insipired quark model