Inclusive Decay Distributions of Coherent Two-Body States

When a vector meson such as φ, J/Ψ(3S), or ϒ(4S) decays to a particle-antiparticle pair of neutral mesons, the time distribution of inclusive decay to a given final state is naively expected to be the incoherent sum of those of the two mesons with opposite flavors. In this paper, we show that this is in general not the case for arbitrary coherent two-body states and obtain conditions under which such a naive incoherent sum gives the correct distributions. In particular, the condition is satisfied by any linear superposition of B⁰B̅ ⁰ and B̅ ⁰B⁰. The analysis is applicable to the cases with more than two orthogonal states.