$K\to \pi \nu \bar{\nu }$ and High Precision Determinations of the CKM Matrix

Abstract

We investigate the future determination of the CKM matrix using theoretically clean quantities, like $B(K^{+}\to {\pi }^{+}\nu \bar{\nu })$, $B(K_L\to {\pi }^0\nu \bar{\nu })$ or $\sin 2\beta$, $\sin 2\alpha$ as extracted from CP violation studies in $B$ physics. The theoretical status of $K\to \pi \nu \bar{\nu }$ is briefly reviewed and their phenomenological potential is compared with that of CP asymmetries in $B$ decays. We stress the unique opportunities provided by measuring the CP violating rare decay $K_L\to {\pi }^0\nu \bar{\nu }$. It is pointed out that this mode is likely to offer the most precise determination of $\mathrm{Im}{V}_{ts}^{\ast }{V}_{td}$ and the Jarlskog parameter $J_{CP}$, the invariant measure of CP violation in the Standard Model.

Comments: LaTeX, 15 pages, 2 figures