New Physics and Evidence for a Complex CKM

We carefully 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 $\Delta I=1/2$pieceof$B\to\rho\rho$and$B\to\rho\pi$. We emphasize the crucial r^ ole played by the angle $\gamma$ in both providing irrefutable evidence for a 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%.