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 data are used to place bounds upon parameter space. We then examine flavonstrahlung (${Z^\prime}^\ast \rightarrow Z^\prime \vartheta$ 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.