Diagrammatic Analysis of Charmless Three-Body B Decays

TL;DR

This paper develops a diagrammatic approach to analyze charmless three-body B decays, enabling extraction of decay amplitudes and weak-phase information, with current data supporting the Standard Model predictions.

Contribution

It introduces a method to express three-body B decay amplitudes diagrammatically and demonstrates how to extract weak-phase information from these decays.

Findings

Current data agree with Standard Model predictions.

It is possible to extract weak-phase information from three-body decays.

Neglecting annihilation diagrams modifies isospin-based results.

Abstract

We express the amplitudes for charmless three-body B decays in terms of diagrams. In addition, we show how to use Dalitz-plot analyses to obtain decay amplitudes which are symmetric or antisymmetric under the exchange of two of the final-state particles. When annihilation-type diagrams are neglected, as in two-body decays, many of the exact, purely isospin-based results are modified, leading to new tests of the standard model (SM). Some of the tests can be performed now, and we find that present data agree with the predictions of the SM. Furthermore, contrary to what was thought previously, it is possible to cleanly extract weak-phase information from three-body decays, and we discuss methods for B -> K pi pi, K K Kbar, K Kbar pi and pi pi pi.