Flavonstrahlung in the $B_3-L_2$ $Z^{\mathrm{\prime }}$ Model at Current and Future Colliders

The $B_3-L_2$ $Z^{\mathrm{\prime }}$ model may explain some gross features of the fermion mass spectrum as well as $b\to s\mathrm{\ell }\mathrm{\ell }$ anomalies. A TeV-scale physical scalar field associated with gauged $U(1{)}_{B_3-L_2}$ spontaneous symmetry breaking, the flavon field $\vartheta$, 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 ($Z^{\mathrm{\prime }}\to Z^{\mathrm{\prime }}\vartheta$ production) at colliders as a means to directly produce and discover flavon particles, providing direct empirical evidence tying it 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.