CP Violation in B Decays within QCD Factorization

Abstract

We analyze the extraction of weak phases from CP violation in $B\toπ^+π^-$ decays. By combining the information on mixing induced CP violation in $B\toπ^+π^-$, namely $S_{ππ}$, with the precision observable $\sin 2β$ obtained from the ``gold-plated''mode $B\toψK_S$, we propose the determination of the unitarity triangle. We also discuss alternative ways to analyze $S_{ππ}$ which can be useful if new physics affects $B_d$--$\bar B_d$ mixing. Predictions and uncertainties for $r$ and $ϕ$ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in $1/m_b$ and $1/N_C$ leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed.