B-Decay CP Asymmetries, Discrete Ambiguities and New Physics

The first measurements of CP violation in the B system will likely probe $\sin 2\alpha$, $\sin 2\beta$ and $\cos 2\gamma$. Assuming that the CP angles $\alpha$, $\beta$ and $\gamma$ are the interior angles of the unitarity triangle, we show that these measurements determine the angle set $(\alpha,\beta,\gamma)$ except for a twofold discrete ambiguity. If one allows for the possibility of new physics, the presence of this discrete ambiguity can make its discovery difficult: if only one of the two candidate 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. We examine the values of $(\alpha,\beta,\gamma)$ and the new-physics parameters for which this scenario can arise, and discuss ways to resolve the discrete ambiguity. The discrete ambiguity resolution often, but not always, helps to uncover the new physics.