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The production of fully-heavy tetraquark states in proton-proton ($pp$) andproton-nucleus ($pA$) collisions at the center-of-mass energies of the LargeHadron Collider (LHC) and at the Future Circular Collider (FCC) is investigatedconsidering that these states are produced through the double parton scatteringmechanism. We estimate the cross sections for the $T_{4c}$, $T_{4b}$ and$T_{2b2c}$ states and present predictions for $pp$, $pCa$ and $pPb$ collisionsconsidering the rapidity ranges covered by central and forward detectors. Wedemonstrate that the cross sections for $pA$ collisions are enhanced incomparison to the $pp$ predictions scaled by the atomic number. Moreover, ourresults indicate that a search of these exotic states is, in principle,feasible in the future runs of the LHC and FCC.

Production of fully-heavy tetraquark states through the double parton scattering mechanism in $pp$ and $pA$ collisions