$K^+\to \pi^+\nu\bar\nu$: a rising star on the stage of flavour physics

Abstract

Motivated by the new experimental information reported by the BNL--E787 Collaboration, we analyse the present impact and the future prospects opened by the measurement of $\br(K^+\to\pi^+\nu\bar\nu)$. Although still affected by a large error, the BNL--E787 result favours values of $\br(K^+\to \pi^+\nu\bar\nu)$ substantially larger than what expected within the Standard Model. As a result, this data already provide non-trivial constraints on the unitarity triangle, when interpreted within the Standard Model framework. We stress the importance of the clean relation between $\br(K^+\to \pi^+\nu\bar\nu)$, $\sin2\beta$ and $\Delta M_{B_d}/\Delta M_{B_s}$ that in the next few years could provide one of the deepest probes of the Standard Model in the sector of quark-flavour dynamics. A speculative discussion about possible non-standard interpretations of a large $\br(K^+\to \pi^+\nu\bar\nu)$ is also presented. Two main scenarios naturally emerge: those with direct new-physics contributions to the $s \to d \nu\bar\nu$ amplitude and those with direct new-physics effects only in $B_d$--$\bar B_d$ mixing. Realistic models originating these two scenarios and possible future strategies to clearly identify them are briefly discussed.