B physics: CP violation beyond the SM

We analyse the present experimental evidence for a complex CKM matrix, even allowing for New Physics contributions to $\epsilon_{K}$, $a_{J/\Psi K_{S}}$%, $\Delta M_{B_{d}}$, $\Delta M_{B_{s}}$, and the $\Delta I=1/2$ piece of $% B\to \rho \rho $ and $B\to \rho \pi $. We emphasize the crucial r\^{o}le played by the angle $\gamma $ in both providing irrefutable evidence for a 3$\times $3 complex CKM matrix and placing constraints on the size of NP contributions. It is shown that even if one allows for New Physics a real CKM matrix is excluded at a 99.92% C.L., and the probability for the phase $\gamma $ to be in the interval $[-170^{\circ};-10^{\circ}]\cup \lbrack 10^{\circ};170^{\circ}]$ is 99.7%. Large value of the phase $\chi $, e.g. of order $\lambda $, is only possible in models where the unitarity of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix is violated through the introduction of extra $Q=2/3$ quarks. We study the allowed range for $\chi $ and the effect of a large $\chi $ on various low-energy observables, such as CP asymmetries in $B$ meson decays. We also discuss the correlated effects which would be observable at high energy colliders, like decays $t\to cZ$, etc..