Muon decay asymmetries fromKL0→π0μ+μ−decays

We examine the decay $K_L^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$ in which the branching ratio, the muon energy asymmetry and the muon decay asymmetry could be measured. In particular, we find that within the standard model the longitudinal polarization ${(P}_L)$ of the muon is proportional to the direct $\mathrm{CP}$ violating amplitude. On the other hand the energy asymmetry and the out-of-plane polarization ${(P}_N)$ depend on both indirect and direct $\mathrm{CP}$ violating amplitudes. Although the branching ratio is small and difficult to measure because of the background, the asymmetries could be as large as $\mathcal{O}\mathrm{}\left(1\right)\mathrm{}$ in the standard model. A combined analysis of the energy asymmetry, $P_L,$ and $P_N$ could be used to separate indirect CPV, direct CPV, and $\mathrm{CP}$ conserving contributions to the decay.