Polarization and Correlation Effects in Lepton Flavor Violated Decays Induced by Axion-Like Particle

Lepton flavor violated processes are strongly suppressed in the Standard Model, but can be sizable in some extended models. The current experimental bounds on decay modes $\ell'^{\pm} \to a \ell^{\pm}$ are much weaker than the other processes because of the huge irreducible backgrounds $\ell'^{\pm} \to \ell^{\pm} \bar{\nu}_{\ell} \nu_{\ell'}$. In this paper, we study polarization effects of both the signals and backgrounds. We find that signals and backgrounds have distinctive polarization effects, and for the irreducible backgrounds both longitudinal and transverse polarization effects survive when the relative momentum of the two neutrinos are integrated out. At low energy $e^+e^-$ collider, for instance the Belle II experiment, leptons are generated in pair but with no net polarization. However, we show that polarization correlation of the lepton pair is a useful observable for probing the signal. More interestingly, the polarization correlation depends on product of scalar and pseudo-scalar couplings, and hence are sensitive to their relative sign. Because kinematical reconstruction or tagging is not necessary, number of the available signal events increases significantly.