NewCP-violating parameters in cascade decays

We consider decay chains of the type $\overrightarrow{P}M+\cdot \cdot \overrightarrow{\cdot }f+\cdot \cdot \cdot ,$ where M is a neutral meson that may mix with its antiparticle $\overline{M},$ before decaying into the final state f. Here P may be either a heavier neutral meson or a charged meson. We perform a rephasing-invariant analysis of the quantities that show up in such cascade decays. If the decay $\overrightarrow{P}M+\cdot \cdot \cdot$ (or the decay $\overrightarrow{P}\overline{M}+\cdot \cdot \cdot )$ is forbidden, we find the usual ${\lambda }_f$ parameters describing the interference between the mixing of a neutral meson system and the decay from that system into the final state f. However, when both the $\overrightarrow{P}M+\cdot \cdot \cdot$ and $\overrightarrow{P}\overline{M}+\cdot \cdot \cdot$ decays are allowed, we find a new class of rephasing-invariant parameters, ${\xi }_i,$ which measure the interference between the mixing of a neutral meson system and the decay from the initial state into that system. We show that the quantities ${\lambda }_f$ and ${\xi }_i$ are necessary and sufficient to describe all the interference effects present in the most general cascade decay. We discuss the various cascade decays in turn, highlighting the special features of each one.