Determination of weak phases $ϕ_2$ and $ϕ_3$ from $B\to ππ,Kπ$ in the pQCD method

Abstract

We look at two methods to determine the weak phases $ϕ_2$ and $ϕ_3$ from $B \to ππ$ and $Kπ$ decays within the perturbative QCD approach. We obtain quite interesting bounds on $ϕ_2$ and $ϕ_3$ from experimental measurements in asymmetric B-factory: $55^o \leq ϕ_2 \leq 100^o$ and $51^o \leq ϕ_3 \leq 129^o$. Specially we predict the possibility of large direct CP violation effect in $B^0 \to π^{+}π^{-}$ decay with $A_{cp}^{dir}(B\to π^{+} π^{-})=(23\pm7)$ %.