Implications of $K\toπν\barν$ for new physics in $B$ decays

The new measurement of the $K^+\to\pi^+\nu\bar\nu$ branching ratio by the NA62 collaboration represents an important milestone in precision flavour physics. Under different flavour assumptions on beyond the standard model physics, this decay mode can be related to many other observables with underlying flavour-changing currents, such as $B\to K\nu\bar\nu$ or $B_s\to\mu\mu$, effectively providing an additional handle in our exploration of flavour-violating new physics effects. We study the impact of this new result, under the hypotheses that deviations from the standard model arise from modified $Z$ couplings, or from effects in semileptonic interactions. Finally, we review the implications of our scenarios for the yet to be measured partner mode $K_L\to\pi^0\nu\bar\nu$.