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Rare $K \to \pi \nu \bar \nu$ decays, being dominated by short distancecontributions within the Standard Model (SM), open a window for New Physics(NP) searches at low energies. The $ K \to \pi \nu \bar\nu $ branching ratiosare expected to be measured with $ \sim 10\% $ accuracies by NA62/CERN andKOTO/JPARC. The theoretical uncertainties of branching ratios within the SM arewell under control. In the $ B $ sector, it is tentative to explain the $ B$-meson anomalies $ R_{D^{(\ast)}} $ and/or $ R_{K^{(\ast)}} $ by effects ofphysics beyond the SM. Although NP seems to be present in the third fermiongeneration it might also manifest in the flavor changing neutral currenttransition $ s \to d $. Together with the anticipated good experimentalsensitivities and accurate theoretical predictions for $ K\to \pi \nu \bar \nu$, this motivates studies of correlated effects of NP in rare $ K\to \pi \nu\bar \nu $ and $ B \to K^{(*)} \mu^+ \mu^- $ decays. Here we consider the loopinduced effects in $ K \to \pi \nu \bar\nu $ in two leptoquark models designedto address lepton-flavor universality violation in the $ R_{K^{(\ast)}} $anomalies.

Footprints of leptoquarks: from $ R_{K^{(*)}} $ to $ K \to \pi \nu \bar\nu $