Inelastic final-state interaction

TL;DR

This paper investigates the complexities of final-state interactions in multichannel decays, especially in B meson decays, highlighting the limitations of existing theorems and proposing an approximation method for dominant inelastic channels.

Contribution

It introduces a new approximation method for analyzing inelastic final-state interactions when one channel dominates, applied specifically to B to pi K decays.

Findings

The Watson theorem does not hold for multichannel final states.

An approximation method for dominant inelastic channels is proposed.

Insights into strong phases in B decays are obtained despite limited data.

Abstract

The final-state interaction in multichannel decay processes is sytematically studied with application to B decay in mind. Since the final-state inteaction is intrinsically interwoven with the decay interaction in this case, no simple phase theorem like "Watson's theorem" holds for experimentally observed final states. We first examine in detail the two-channel problem as a toy-model to clarify the issues and to remedy common mistakes made in earlier literature. Realistic multichannel problems are too challenging for quantitative analysis. To cope with mathematical complexity, we introduce a method of approximation that is applicable to the case where one prominant inelastic channel dominates over all others. We illustrate this approximation method in the amplitude of the decay B to pi K fed by the intermediate states of a charmed meson pair. Even with our approximation we need more accurate information of strong interactions than we have now. Nonethless we are able to obtain some insight in the issue and draw useful conclusions on general fearyres on the strong phases.