Precise Determinations of the CKM Matrix from CP-Asymmetries in B-Decays and K_L --> \pi^0 \nu \bar\nu

Abstract

We point out that the measurements of the CP asymmetries in neutral B-decays together with a measurement of $Br(K_L\to \pi^\circ\nu\bar\nu)$ and the known value of $\mid V_{us}\mid $ can determine {\it all} elements of the Cabibbo-Kobayashi-Maskawa matrix without essentially any hadronic uncertainties. In particular the strong dependence of $Br(K_L\to \pi^\circ\nu\bar\nu)$ on $\mid V_{cb}\mid$ ($\mid V_{cb}\mid^4$) can be used to determine this element precisely. Consequently $\mid V_{ub}\mid$, $\mid V_{td}\mid$ and $\mid V_{ts} \mid $ can also be determined. We derive a set of formulae which facilitate this study and we present a numerical analysis of several future scenarios. Accurate determinations of all parameters are expected from the B-factories and the Main Injector era at Fermilab including KAMI. An impressive accuracy should be reached in the LHC era. An analysis using $Br(\kpnn)$ instead of $Br(\klpnn)$ shows that although the determination of $\mid V_{cb}\mid$ and $\mid V_{td}\mid$ this way is less accurate, still useful results for these elements can be obtained.