Test of factorisation in $B \to K\pi$ decays

TL;DR

This paper tests the factorisation model in B to K pi decays, deriving relations for branching ratios and CP-averaged decay rate ratios to evaluate the model's validity and estimate the weak angle gamma.

Contribution

It introduces a relation for branching ratios independent of strong penguin interactions and suggests using decay rate ratios to test factorisation and determine gamma.

Findings

Factorisation qualitatively describes CLEO data.

Derived a branching ratio prediction for B0 to K0 pi0.

Suggested decay rate ratios can test the model and estimate gamma.

Abstract

We analyse the $B \to K\pi$ decays using the factorisation model with final state interaction phase shift included. We find that factorisation seems to describe qualitatively the latest CLEO data. For a test of the factorisation model, we derive a relation for the branching ratios independent of the strength of the strong penguin interactions. This relation gives a central value of $(0.60 \times 10^{-5})$ for ${\mathcal B}(\bar{B}^{0} \to \bar{K}^{0}\pi^{0})$, somewhat smaller than the latest CLEO measurement, but the experimental errors are yet too big to take it as a real prediction of the factorisation model. We also find that a ratio obtained from the CP-averaged $B \to K\pi$ decay rates could be used to test the factorisation model and to determine the weak angle $\gamma$ with more precise data, though the l atest CLEO data seem to favor $\gamma$ in the range of $(90^{\circ}-120^{\circ})$.