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

The $B_3-L_2$ $Z^\prime$ model may explain some gross features of the fermion mass spectrum as well as $b\rightarrow s \ell \ell$ 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 (${Z^\prime} \rightarrow Z^\prime \vartheta$ 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.