Measurements of the ρ and η parameters of the V_CKM 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 ρ and η parameters. From this study it follows that, in the Standard Model, the B_s⁰-B̄_s⁰ oscillation frequency, Δm_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 Δm_s 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 2β = 0.67_-0.13^+0.12 is obtained. So far no constraint can be obtained on sin 2α. The interest of having a direct measurement of sin 2α and sin 2β 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.