How could we test for extra dimensions? One option would be to find evidence of particles that can exist only if extra dimensions are real. Theories that suggest extra dimensions predict that, in the same way as atoms have a low-energy ground state and excited high-energy states, there would be heavier versions of standard particles in other dimensions. These heavier versions of particles – called Kaluza-Klein states – would have exactly the same properties as standard particles (and so be visible to our detectors) but with a greater mass. If CMS or ATLAS were to find a Z- or W-like particle (the Z and W bosons being carriers of the electroweak force) with a mass 100 times larger for instance, this might suggest the presence of extra dimensions. Such heavy particles can only be revealed at the high energies reached by the Large Hadron Collider (LHC).
https://home.cern/about/physics/extra-dimensions-gravitons-and-tiny-black-holes