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We have examined the decay $K^0_L \to \pi^0 \mu^+ \mu^-$ in which thebranching ratio, the muon energy asymmetry and the muon decay asymmetry couldbe measured. In particular, we find that within the Standard Model thelongitudinal polarization ($P_L$) of the muon is proportional to the direct CPviolating amplitude. On the other hand the energy asymmetry and theout-of-plane polarization ($P_N$) depend on both indirect and direct CPviolating amplitudes. Although the branching ratio is small and difficult tomeasure because of background, the asymmetries could be large $\cal{O}$(1) inthe 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 conservingcontributions to the decay.Comment: 6 pages, 4 figures, To be Published in Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Muon decay asymmetries from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:…

Muon decay asymmetries fromKL0→π0μ+