Past exam of the particle physics course of the University of Oxford / 2022 / 2 / b / Solution

Choose the exchange-positive CP convention for neutral kaon mixing, $CP|K^0⟩=|{\bar{K}}^0⟩$. Neglecting CP violation, the kaon CP eigenstates can then be writtenWriting $A=A({\bar{D}}^0\to K^0{\pi }^0)$ and $B=A({\bar{D}}^0\to {\bar{K}}^0{\pi }^0)$, projection on these coherent final states givesThis is the convention implicit in the printed sum. Changing the sign convention for the neutral antikaon changes both its coefficient in the kaon CP eigenstates and $B$; it cannot change either physical decay rate. The extremely small $K_S$–$K_L$ mass difference can be ignored in the two-body phase space.