The final-state interaction in the two-body nonleptonic decay of a heavy particle

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We attempt to understand the final-state interaction in the two-body nonleptonic decay of a heavy particle for which many multibody decay channels are also open. No matter how many multibody channels couple to the two-body channels, the analyticity of the S-matrix relates the phase and the magnitude of the two-body decay amplitude through a dispersion relation. In general, however, the phase cannot be determined by strong interactions alone. The dispersion relation requires on a general ground that the final-state interaction phases be small for the two-body decay amplitudes when the initial particle is very heavy. We then analyze the final-state interaction phases in terms of the s-channel eigenstates of the S-matrix and obtain semiquantitative results applicable to the B decay with a random S-matrix hypothesis. We use the high-energy scattering date and the dual resonance model as a guide to the relevant aspects of strong interactions at long and intermediate distances.