B -decay CP asymmetries, discrete ambiguities, and new physics

The first measurements of CP violation in the B system will likely probe $\mathrm{sin}2\ensuremath{\alpha},$ $\mathrm{sin}2\ensuremath{\beta},$ and $\mathrm{cos}2\ensuremath{\gamma}.$ Assuming that the CP angles \ensuremath{\alpha}, \ensuremath{\beta}, and \ensuremath{\gamma} are the interior angles of the unitarity triangle, these measurements determine the angle set (\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\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 or not new physics is present. We review the methods used to resolve the discrete ambiguity and show that, even in the presence of new physics, they can usually be used to uncover this new physics. There are some exceptions, which we describe in detail. We systematically scan the parameter space and present examples of values of (\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma}) and the new-physics parameters which correspond to all possibilities. Finally, we show that if one relaxes the assumption that the bag parameters ${B}_{{B}_{d}}$ and ${B}_{K}$ are positive, one can no longer definitively establish the presence of new physics.