How well can we predict CP asymmetry in $B\to ππ$, $Kπ$ decays?

Abstract

Using the perturbative QCD amplitudes for $B\to ππ$ and $B\to Kπ$, we have performed an extensive study of the parameter space where the theoretical predictions for the branching ratios are consistent with recent experimental data. From this allowed range of parameter space, we predict the mixing induced CP asymmetry for $B \to π^+π^-$ with about 11% uncertainty and the other CP asymmetries for $B\to ππ$, $Kπ$ with 40% ~ 47% uncertainty. These errors are expected to be reduced as we restrict the parameter space by studying other decay modes and by further improvements in the experimental data.