Bounding the effect of penguin diagrams in $a_{CP}(B^0\to {\pi }^{+}{\pi }^{-})$

Abstract

A clean determination of the angle $\alpha$ of the unitary triangle from $B\to \pi \pi$ decays requires an isospin analysis. If the $B\to {\pi }^0{\pi }^0$ and $\bar{B}\to {\pi }^0{\pi }^0$ decay rates are small it may be hard to carry out this analysis. Here we show that an upper bound on the error on $\sin 2\alpha$ due to penguin diagram effects can be obtained using only the measured rate $\text{BR}(B^{\pm }\to {\pi }^{\pm }{\pi }^0)$ and an upper bound on the combined rate $\text{BR}(B\to {\pi }^0{\pi }^0)+\text{BR}(\bar{B}\to {\pi }^0{\pi }^0)$. Since no b flavor tagging is needed to measure this combined rate, the bound that can be achieved may be significantly better than any approach which requires separate flavor-tagged neutral pion information.

Comments: 10 pages, revtex + axodraw, 2 figures included