Search for lepton-flavor-violating ALPs at a future muon collider and utilization of polarization-induced effects

Axion-Like Particles (ALPs) are pseudo Nambu-Goldstone bosons associated with spontaneously broken global $U(1)$ symmetries. Such particles can have lepton-flavor-violating (LFV) couplings to the SM charged leptons. LFV ALPs provide the possibility to address some of the SM long-lasting problems. We investigate the sensitivity of a future muon collider suggested by the Muon Accelerator Program (MAP) to the production of LFV ALPs in the ALP mass range $m_a\leq1$ MeV. ALPs are assumed to be produced through the LFV decay $\tau\ra\ell a$ ($\ell=e,\mu$) of one of the tau leptons produced in the muon-anti muon annihilation. Performing a realistic detector simulation and deploying a multivariate technique, we constrain the LFV couplings $c_{\tau e}$ and $c_{\tau \mu}$ for both the cases of unpolarized and polarized muon beams. Three different chiral structures are considered for the LFV ALP coupling and the muon collider is assumed to operate at the center-of-mass energies of 126, 350 and 1500 GeV. We present a procedure to search for LFV ALPs at colliders which takes advantage of tau polarization-induced effects. Polarized tau leptons which produce such effects can be produced when the initial muon beams are polarized. Utilizing the properties of polarized tau decays, the main SM background which overwhelms the ALP production in the case of unpolarized muon beams can be significantly suppressed. We present 95$\%$ CL expected limits on the LFV couplings and show that the present analysis can improve current experimental limits on the ALP LFV couplings by roughly one order of magnitude.