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

Abstract

A clean determination of the angle $α$ of the unitary triangle from $B\to ππ$ decays requires an isospin analysis. If the $B \to π^0π^0$ and $\bar B \to π^0π^0$ decay rates are small it may be hard to carry out this analysis. Here we show that an upper bound on the error on $\sin 2α$ due to penguin diagram effects can be obtained using only the measured rate $\BR(B^\pm \to π^\pm π^0)$ and an upper bound on the combined rate $\BR(B \to π^0 π^0) + \BR(\bar B \to π^0 π^0)$. 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.