Measurements of the ρ and η parameters of the Vckm Matrix and Perspectives

A review of the current status of the Cabibbo-Kobayashi-Maskawa matrix (V-CKM) is presented and a special emphasis is put on the determination of the rho and eta parameters. From this study it follows that, in the Standard Model the B-s(0)-<(B-s(0))over bar> oscillation frequency, Delta m(s), has to lie with 68% C.L., between 6.5 ps(-1) and 15 ps(-1), and is below 21 ps(-1) at 95% C.L. If the interest of measuring Am, is underlined, the importance of a precise determination of the B meson decay constant, f(B), is also stressed. It is also proposed to obtain a precise value for this parameter from an accurate measurement of f(D), the D meson decay constant, using results from lattice QCD to relate D and B hadrons. A future Tau-Charm factory could accomplish this task. It is also shown that from the present measurements, assuming the validity of the Standard Model an already accurate value of sin 2 beta = 0.67(-0.13)(+0.12) is obtained So far no constraint can be obtained on sin 2 alpha. The interest of having a direct measurement of sin 2 alpha and sin 2 beta at B-factories or at other facilities is reminded. Finally, constraints on SUSY parameters, in the framework of a given model obtained from a precise measurement of the CKM matrix elements are analyzed.