Finding flavons at colliders

We conduct a comprehensive investigation into the flavour phenomenology and collider signatures of flavon of ZN × ZM flavour symmetries for the soft symmetry-breaking scenario and a new symmetry-conserving mechanism at the high-luminosity LHC, high energy LHC, and a 100 TeV hadron collider. The flavour physics of quark and leptonic observables places different bounds on the parameter space of flavons of ZN × ZM flavour symmetries. On the collider side, the decay t → c a can be probed by the high-luminosity LHC, high energy LHC, and a 100 TeV hadron collider for the Z₈ × Z₂₂ flavour symmetry. The inclusive production signatures can be used to probe the flavon of all the ZN × ZM flavour symmetries for the soft symmetry-breaking scenario for a heavy flavon at a 100 TeV collider. Flavons of all the ZN × ZM flavour symmetries can be probed at high energy LHC and a 100 TeV collider for a low mass in the case of soft symmetry-breaking. The di-flavon production is within reach of the high-luminosity LHC, high energy LHC, and a 100 TeV collider only for a light flavon. The 14 TeV high-luminosity LHC can probe only the Z₂ × Z₅ and Z₈ × Z₂₂ flavour symmetries for a few specific inclusive signatures. The symmetry-conserving scenario remains beyond the detection capabilities of any collider.