How sensitive to FCNC can $B^0$ CP asymmetries be?

We show that the study of CP asymmetries in neutral B-meson decays provides a very sensitive probe of flavour-changing neutral currents (FCNC). We introduce two new angles, $\alpha_{SM}$ and $\beta_{SM}$, whose main feature is that they can be readily obtained from the measurement of the CP asymmetries $a_{J/\psi K_s}$, $a_{\pi^+ \pi^-}$ and the ratio $R_u \equiv|V_{ud}V_{ub}^*|/|V_{cd}V_{cb}^*|$, providing a quantitative test of the presence of new physics in a model-independent way. Assuming that new physics is due to the presence of an isosinglet down-type quark, we indicate how to reconstruct the unitarity quadrangles and point out that the measurements of the above asymmetries, within the expected experimental errors, may detect FCNC effects, even for values of $|\sum_{i=1}^3 V_{id} V_{ib}^* / (V_{td} V_{tb}^*)|$ at the level of a few times $10^{-2}$.