Finding Flavons at Colliders

We conduct a comprehensive investigation into the flavor phenomenology and collider signatures of flavon of ZN x ZM flavor 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 flavor physics of quark and leptonic observables places different bounds on the parameter space of flavons of ZN x ZM flavor symmetries. On the collider side, the decay t -> ca can be probed by the high-luminosity LHC, high-energy LHC, and a 100 TeV hadron collider for the Z8 x Z 22 flavor symmetry. The inclusive production signatures can be used to probe the flavon of all the ZN x ZM flavor symmetries for the soft symmetry-breaking scenario for a heavy flavon at a 100 TeV collider. Flavons of all the ZN x ZM flavor 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 diflavon 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 x Z5 and Z8 x Z 22 flavor symmetries for a few specific inclusive signatures. The symmetry-conserving scenario remains beyond the detection capabilities of any collider.