Muon Decay Asymmetries from $K_L^0\to \ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ Decays

Abstract

We have examined the decay $K_L^0\to \ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ 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 CP violating amplitude. On the other hand the energy asymmetry and the out-of-plane polarization ($P_N$) depend on both indirect and direct CP violating amplitudes. Although the branching ratio is small and difficult to measure because of background, the asymmetries could be large $\mathcal{O}$(1) 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 CP conserving contributions to the decay.

6 pages, 4 figures, To be Published in Physical Review D