Determination of weak phases $\phi_2$ and $\phi_3$ from $B\to \pi\pi,K\pi$ in the pQCD method

Abstract

We look at two methods to determine the weak phases $\phi_2$ and $\phi_3$ from $B \to \pi\pi$ and $K\pi$ decays within the perturbative QCD approach. We obtain quite interesting bounds on $\phi_2$ and $\phi_3$ from recent experimental measurements in asymmetric B-factory: $55^o \leq \phi_2 \leq 100^o$ and $51^o \leq \phi_3 \leq 129^o$. Specially we predict the possibility of large direct CP violation effect in $B^0 \to \pi^{+}\pi^{-}$ decay with $A_{cp}^{dir}(B\to \pi^{+} \pi^{-})=(23\pm7)$ %.Comment: 6 pages, Latex, 3 figures, typos corrected. Presented at Workshop on CKM Unitarity Triangle (CERN 2002-2003), Geneva, Switzerland, 13-16 Feb 200