Difficulties in Obtaining Weak Phases from $b\to d$ Penguin Decays

Abstract

We re-examine a recent proposal for obtaining \beta using the measurements of the b -> d penguin decays B_d(t) -> K^0 \kbar and B_s(t) -> \phi K_S, along with a theoretical assumption. We show that there are in fact three assumptions one can make, so that the method can in principle be used to extract \alpha, \beta or \gamma. We also show that it is the assumption which yields \gamma which is the best. However, the theoretical error on this assumption is still 25-30%, which leads to an error on \gamma of at least 20-25%. Given our current understanding of hadronic physics, it does not seem possible to reduce this error.