Testing the standard model and schemes for quark mass matrices withCPasymmetries inBdecays

The values of $sin2\alpha$ and $sin2\beta$, where $\alpha$ and $\beta$ are angles of the unitarity triangle, will be readily measured in a $B$ factory (and maybe also in hadron colliders). We study the standard model constraints in the $sin2\alpha -\mathrm{s}\mathrm{i}\mathrm{n}2\beta$ plane. We use the results from recent analyses of $f_B$ and ${\tau }_b{\left|V_{\mathrm{cb}}\right|}^2$ which take into account heavy-quark symmetry considerations. We find $sin2\beta \ge 0.15$ and most likely $sin2\beta \gtrsim 0.6$, and emphasize the strong correlations between $sin2\alpha$ and $sin2\beta$. Various schemes for quark mass matrices allow much smaller areas in the $sin2\alpha -sin2\beta$ plane. We study the schemes of Fritzsch, of Dimopoulos, Hall, and Raby, and of Giudice, as well as the "symmetric Cabibbo-Kobayashi-Maskawa" idea, and show how $\mathrm{CP}$ asymmetries in $B$ decays will crucially test each of these schemes.