  We investigate the production of the fully - heavy tetraquark states $T_{4Q}$
in the $\gamma \gamma$ interactions present in proton-proton, proton-nucleus
and nucleus-nucleus collisions at the CERN Large Hadron Collider (LHC). We
focus on the $\gamma \gamma \rightarrow {\cal{Q}}{\cal{Q}}$ (${\cal{Q}} =
J/\psi,\, \Upsilon$) subprocess, mediated by the $T_{4Q}$ resonance in the $s$
- channel, and present predictions for the hadronic cross sections considering
the kinematical ranges probed by the ALICE and LHCb Collaborations. Our results
demonstrate that the experimental study of this process is feasible and can be
used to investigate the existence and properties of the $T_{4c}(6900)$ and
$T_{4b}(19000)$ states.

High Energy Physics - Phenomenology;High Energy Physics - Experiment