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 ${ϵ}_K$, $a_{J\mathrm{/}\mathrm{\Psi }{K}_S}$%, $\mathrm{\Delta }{M}_{B_d}$, $\mathrm{\Delta }{M}_{B_s}$, and the $\mathrm{\Delta }I=1\mathrm{/}2$ 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 $[-{170}^{\circ };-{10}^{\circ }]\cup [{10}^{\circ };{170}^{\circ }]$ 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 $Q=2\mathrm{/}3$ 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…