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

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 $(90^{\circ}-120^{\circ})$.