A Study of Some Methods for Measuring CKM CP Violating Phases

Abstract

We study the influence of penguin (especially, electroweak penguin) effects on some methods of measuring the angles $\alpha$, $\beta$, and $\gamma$ in the CKM unitarity triangle. We use next-to-leading order effective Hamiltonian, and present numerical estimates based on the factorization approximation. We find that some techniques suggested in the literature, especially for $\alpha$ determination, are not workable in light of the electroweak penguin effects. Nevertheless, there are methods that would work for each angle determination. For angle $\beta$ we consider $B \rightarrow D^{+} D^{-}$ mode and estimate the penguin contamination. For angle $\gamma$ we consider a method based on SU(3) symmetry and carefully consider SU(3) breaking effects. We point out regions in the parameter space where this method could be used reliably.