K→πνν¯and high precision determinations of the CKM matrix

We investigate the future determination of the CKM matrix using theoretically clean quantities, such as $B(K^{+}\to {\pi }^{+}\nu \overline{\nu })$, $B(K_L\to {\pi }^0\nu \overline{\nu })$ or $sin2\beta$, $sin2\alpha$ as extracted from $\mathrm{CP}$ violation studies in $B$ physics. The theoretical status of $K\to \pi \nu \overline{\nu }$ is briefly reviewed and their phenomenological potential is compared with that of $\mathrm{CP}$ asymmetries in $B$ decays. We stress the unique opportunities provided by measuring the $\mathrm{CP}$-violating rare decay $K_L\to {\pi }^0\nu \overline{\nu }$. It is pointed out that this mode is likely to offer the most precise determination of Im $V_{\mathrm{ts}}^{*}{V}_{\mathrm{td}}$ and the Jarlskog parameter $J_{\mathrm{CP}}$, the invariant measure of $\mathrm{CP}$ violation in the standard model.