Some Prospects for the Determination of the Unitarity Triangle Before the LHC Era

Abstract

Anticipating improved determinations of $m_t$, $|V_{cb}|$, $|V_{ub}/V_{cb}|$, $B_K$ and $F_B \sqrt{B_B}$ in the next five years we make an excursion into the future in order to find a possible picture of the unitarity triangle, of quark mixing and of CP violation around the year~2000. We then analyse what impact on this picture will result from the measurements of the four possibly cleanest quantities: $BR(K^+ \to \pi^+ \nu \bar\nu)$, $x_d/x_s$, $\sin(2\alpha)$ and $\sin(2\beta)$. In the course of our investigations we extend the analysis of the unitarity triangle beyond the leading order in the Wolfenstein parameter $\lambda$. \\ We will also shortly present the status of direct CP violation in $K \rightarrow \pi\pi$ and $K_{\rm L} \rightarrow \pi^0 e^+ e^-$.