Indirect measurement of the vertex and angles of the unitarity triangle

The precise measurements of the $B_d^0$ oscillation frequency and the limit on the $B_s^0$ one as well as the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|{\mathrm{V}}_{\mathrm{ub}}|$ improve the constraints on the other elements of this matrix. A fit to the experimental data and the theory calculations leads to the determination of the vertex of the unitarity triangle as $\rho {=0.16\mathrm{}}_{-0.07}^{+0.09\mathrm{}},\eta =0.38\mathrm{}\pm \mathrm{0.06.}$ The values of its angles, in their customary definition in terms of sines for $\alpha$ and $\beta ,$ are found to be $\sin 2\alpha {=0.06\mathrm{}}_{-0.42}^{+0.35\mathrm{}},\sin 2\beta =0.75\mathrm{}\pm 0.09,\gamma {=67\mathrm{}}_{-12}^{+11\mathrm{}}°.$ Indirect information on nonperturbative QCD parameters, on the presence of a $\mathrm{CP}$ violating complex phase in the CKM matrix, and on the $B_s^0$ oscillation frequency are also extracted.