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Neutral B meson mixing converts the flavor eigenstates $B^0=\bar{b}d$ and ${\bar{B}}^0=b\bar{d}$ into one another through the weak interaction. The propagating mass eigenstates are $|B_L⟩=p|B^0⟩+q|{\bar{B}}^0⟩$ and $|B_H⟩=p|B^0⟩-q|{\bar{B}}^0⟩$, with $|p{|}^2+|q{|}^2=1$.

In units $\hslash =c=1$, neglect their width difference and take $|q/p|=1$. Evolution of an initial $B^0$ at proper time $t$ gives the undecayed flavour probabilitieswhere $\Delta m=m_H-m_L$ and $\Gamma$ is the common decay width. Their sum is the survival probability, not one.

For a common final state, mixing and direct decay interfere through ${\lambda }_f=(q/p)({\bar{A}}_f/A_f)$. In the Standard Model, $f=J/\psi K_S$ combines a J/psi meson with a short-lived neutral kaon. Neglecting subleading weak amplitudes and small kaon CP violation,Here the $V_{ij}$ are CKM matrix elements; the minus sign reflects the approximate negative CP parity of this specified final state. A different charmonium-kaon final state need not have that same sign.^[ref]

The short-lived neutral kaon $K_S$ is one of the two propagating eigenstates of the effective neutral kaon mixing problem. It is a coherent combination $p|K^0⟩+q|{\overline{K}}^0⟩$, with coefficients depending on the phase convention and normalized so $|p{|}^2+|q{|}^2=1$.

In the limit of exact CP symmetry, it is approximately the CP-even combination and readily decays to two pions; the corresponding long-lived state has different allowed decay channels. Small CP violation makes the exact identification with a CP eigenstate imperfect. The observation of two-pion decays in the nominally long-lived beam was therefore evidence for CP violation, not a redefinition of the short-lived state.^[ref]