Observability of`Cascade Mixing' in B0 --> J/psi K0

Abstract

In high statistics observations of B^o --> J/ψK0, originating from the process Upsilon(4S)--> B0 B0, it should be possible to observe `cascade mixing', where one mixing particle, the B0, turns into another, the K0. This is possible despite the difficulty that the length of the beam crossing region makes a precise definition of the primary vertex impossible. This difficulty is circumvented by using an `away side' tag to specify the initial time. We review the formalism for describing such processes, and first apply it to simple B0 mixing, noting it gives a transparent description for CP and T asymmetries. In particular we show that three different asymmetries of the CP and T type, with neglect of direct CP violation, are given by the same expression. For "cascade mixing" we present predictions for processes of the type B_i --> K_j via J/psi, where in the limit of no direct CP violation each state i or j is determined by a simple tag. There are 16 such simple measureable processes, involving 10 functions of the two time intervals involved. The coefficients of the functions are different for each of the processes and are given in terms of the mass splitting and the CP, T violating parameter of the B0 mass matrix m_2. The results presented here are just consquences of the quantum mechanics of particle mixing and do not involve any particular model of CP violation.