Discrete Ambiguities in B-Decay CP Asymmetries and the Search for New Physics

The first measurements of CP violation in the B system will probably extract $\sin 2\alpha$, $\sin 2\beta$ and $\cos 2\gamma$. Assuming that the CP angles $\alpha$, $\beta$ and $\gamma$ are the interior angles of the unitarity triangle, this determines the angle set $(\alpha ,\beta ,\gamma )$ up to a twofold discrete ambiguity. The presence of this discrete ambiguity can make the discovery of new physics difficult: if only one of the two solutions is consistent with constraints from other measurements in the B and K systems, one is not sure whether new physics is present or not. I present examples of this situation, and discuss ways to resolve the discrete ambiguity.