An Axial $U_A(1)_{L_\mu-L_\tau}$: UV Completion and Experimental Searches
We propose an anomaly-free and renormalizable axial $U_A(1)_{L_\mu-L_\tau}$ model and study its experimental signatures for $A'$ masses from the MeV scale to the TeV scale. The opposite charges of the left- and right-handed charged leptons forbid the usual muon and tau Yukawa interactions. Their masses are instead generated by a singlet scalar and heavy vector-like leptons through a universal-seesaw mechanism. We focus on heavy vector-like leptons, small light--heavy mixing, and $m_s\gtrsim10~\mathrm{GeV}$. In this limit, the observables considered here depend mainly on $(m_{A'},g_X)$, while the other model parameters are restricted by mixing and perturbativity. We confront this benchmark with current experimental searches. For neutrino trident production, our finite-$m_\mu$ calculation shows that $A'$ modifies the axial weak coefficient, rather than the vector coefficient relevant to the usual $L_\mu-L_\tau$ model. The longitudinal mode enhances muon bremsstrahlung and gives a negative contribution to $(g-2)_\mu$; the latter dominates over the scalar contribution in our benchmark. Combining these results with invisible meson decays and four-muon resonance searches, we summarize the phenomenological constraints in the $(m_{A'},g_X)$ plane. For $m_{A'}\gg m_\mu$, vector and axial final-state-radiation rates become nearly identical, so the corresponding collider limits can be obtained by rate matching. At a future muon collider, the total rate alone does not fully resolve the interaction structure, whereas angular distributions, especially the forward--backward asymmetry in $\mu^+\mu^-\to\tau^+\tau^-$, retain direct sensitivity to chirality.