Implications of B meson decay data -- a graphical approach

Abstract

The considerable influx of new data on B decays offers opportunities to determine some of the smaller contributions to the decay process, such as suppressed diagrams, and to test the relations between decay amplitudes implied by (broken) SU(3) symmetry. The graphical decomposition of decay amplitudes, corrected here for the contribution of electroweak penguins following Gronau, Rosner et al, implies bounds not only on the size of diagram contributions but also on the relevant complex phases due to Cabbibo-Kobayashi-Maskawa matrix factors. The available data on B decays to two charmless pseudoscalar mesons are analysed to study some of these decay amplitude relations, and allowed values of $γ=Arg(V_{ub}^*)$ which are consistent with the current favoured values is obtained. Our analysis is based on a graphical approach, which offers some insight that is difficult to obtain from $χ^2$ minimisation, and our results are consistent with recent observations on the difficulty of obtaining simultaneous fits to $Kπ$ and $ππ$ decay channels. We have also analyzed the $Kη$ and $Kη'$ channels, and find similar difficulties.