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

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 by means of a non-relativistic quark model based on lattice-QCD studies of the two-body $Q\bar{Q}$ interaction, which exhibits a spin-independent Cornell potential along with a spin-spin term. The four-body problem is solved using the Gaussian expansion method; additionally, the so-called complex scaling technique is employed so that bound, resonance, and scattering states can be treated on the same footing. Moreover, a complete set of four-body configurations, including meson-meson, diquark-antidiquark, and K-type configurations, as well as their couplings, are considered for spin-parity quantum numbers $J^{P(C)}=0^{+(+)}$, $1^{+(\pm)}$, and $2^{+(+)}$ in the $S$-wave channel. Several narrow resonances, with two-meson strong decay widths less than 30 MeV, are found in all of the tetraquark systems studied. Particularly, the fully-charm resonances recently reported by the LHCb Collaboration, 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 the fully-bottom tetraquark spectrum, resonances with masses between 18.9 and 19.6 GeV are found. For the remaining charm-bottom cases, the masses are obtained within a energy region from 9.8 GeV to 16.4 GeV. All these predicted resonances can be further examined in future experiments.