$K^+\to π^+ν\barν$: a rising star on the stage of flavour physics

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 $\br(K^+\toπ^+ν\barν)$. Although still affected by a large error, the BNL--E787 result favours values of $\br(K^+\to π^+ν\barν)$ 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 $\br(K^+\to π^+ν\barν)$, $\sin2β$ and $ΔM_{B_d}/ΔM_{B_s}$ 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 $\br(K^+\to π^+ν\barν)$ is also presented. Two main scenarios naturally emerge: those with direct new-physics contributions to the $s \to d ν\barν$ 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.

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