Determination of weak phases ${\varphi }_2$ and ${\varphi }_3$ from $B\to \pi \pi ,K\pi$ in the pQCD method

Abstract

We look at two methods to determine the weak phases ${\varphi }_2$ and ${\varphi }_3$ from $B\to \pi \pi$ and $K\pi$ decays within the perturbative QCD approach. We obtain quite interesting bounds on ${\varphi }_2$ and ${\varphi }_3$ from recent experimental measurements in asymmetric B-factory: $55^o\le {\varphi }_2\le 100^o$ and $51^o\le {\varphi }_3\le 129^o$. Specially we predict the possibility of large direct CP violation effect in $B^0\to {\pi }^{+}{\pi }^{-}$ decay with $A_{cp}^{dir}(B\to {\pi }^{+}{\pi }^{-})=(23\pm 7)$ %.

6 pages, Latex, 3 figures, typos corrected. Presented at Workshop on CKM Unitarity Triangle (CERN 2002-2003), Geneva, Switzerland, 13-16 Feb 2002