Past exam of the particle physics course of the University of Oxford / 2018 / 3 / e / Solution

Assume the usual semileptonic flavour selection rule $\Delta S=\Delta Q$, negligible wrong-sign decay probability amplitudes, and equal magnitudes for CP-conjugate allowed probability amplitudes. Then $f_{+}={\pi }^{-}{\ell }^{+}\nu$ is reached directly only from $K^0$, and $f_{-}={\pi }^{+}{\ell }^{-}\bar{\nu }$ only from ${\bar{K}}^0$. Put $|A_{f_{+}}|=|{\bar{A}}_{f_{-}}|=|A|$. The four rates areThere is only one path to each tagged semileptonic channel, so no direct/mixed decay interference survives. The semileptonic wrong-sign mixing asymmetry isIt isolates CP violation in mixing under the stated assumptions. Allowing direct semileptonic CP violation or wrong-sign probability amplitudes would spoil that isolation.^[ref]