Kaon CP eigenstates ($CP|K_{1,2}⟩=\pm |K_{1,2}⟩$)

The CP eigenstates of neutral kaons depend on a flavor-state phase convention. Using $CP|K^0⟩=-|{\bar{K}}^0⟩$, set $|K_1⟩=(|K^0⟩-|{\bar{K}}^0⟩)/\sqrt{2}$ and $|K_2⟩=(|K^0⟩+|{\bar{K}}^0⟩)/\sqrt{2}$. They are respectively CP even and odd. Reversing the flavor-exchange sign reverses which written sum is even; it does not change the CP eigenvalues. With CP violation, the physical short- and long-lived states need not equal these CP eigenstates; kaon CP mixing parameter and neutral-kaon CP impurity and two-pion decay describe the mixtures.