Flavonstrahlung in the $B_3-L_2$$Z'$ Model at Current and Future Colliders

The B$_{3}$− L$_{2}$Z′ model may explain some gross features of the fermion mass spectrum as well as b → sℓℓ anomalies. A TeV-scale physical scalar field associated with gauged $ U{(1)}_{B_3-{L}_2} $ spontaneous symmetry breaking, the flavon field ϑ, affects Higgs phenomenology via mixing. In this paper, we investigate the collider phenomenology of the flavon field. Higgs and W boson mass data are used to place bounds upon parameter space. We then examine flavonstrahlung (Z′ → Z′ϑ production) at colliders as a means to directly produce and discover flavon particles, which would provide direct empirical evidence tying the flavon to $ U{(1)}_{B_3-{L}_2} $ symmetry breaking. A 100 TeV FCC-hh or a 10 TeV muon collider would have high sensitivity to flavonstrahlung, whereas the HL-LHC can observe it only in extreme corners of parameter space.