Is it possible to Measure the Weak Phase of a Penguin Diagram?

Abstract

The $b\to d$ penguin amplitude receives contributions from internal $u$, $c$ and $t$-quarks. We show that it is impossible to measure the weak phase of any of these penguin contributions without theoretical input. However, a single assumption involving the hadronic parameters makes it possible to obtain the weak phase and test for the presence of new physics in the $b\to d$ flavour-changing neutral current.