Model-independent Constraints on the Weak Phase $\alpha$ (or ${\varphi }_2$) and QCD Penguin Pollution in $B\to \pi \pi$ Decays

Abstract

We present an {\it algebraic} isospin approach towards a more straightforward and model-independent determination of the weak phase $\alpha$ (or ${\varphi }_2$) and QCD penguin pollution in $B\to \pi \pi$ decays. The world averages of current experimental data allow us to impose some useful constraints on the isospin parameters of $B\to \pi \pi$ transitions. We find that the magnitude of $\alpha$ (or ${\varphi }_2$) extracted from the indirect CP violation in ${\pi }^{+}{\pi }^{-}$ mode is in agreement with the standard-model expectation from other indirect measurements, but its four-fold discrete ambiguity has to be resolved in the near future.

Comments: 11 pages, 3 figures, 2 tables