Inclusive Decay Distributions of Coherent Two-body States

When a vector meson such as phi, J/\Psi(3S) or Upsilon(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 of the mesons, and obtain conditions under which such a naive incoherent sum gives the correct distributions. The analysis is based on the Weisskopf-Wigner formalism, and applicable to the cases where there are more than two orthogonal states that can mix to form a set of eigenstates of mass and decay rate.