Footprints of leptoquarks: from R K ( ∗ ) to K → π ν ν

Rare K→πνν¯ decays, being dominated by short distance contributions within the standard model (SM), open a window for new physics (NP) searches at low energies. The K→πνν¯ branching ratios are expected to be measured with ∼10% accuracies by NA62/CERN and KOTO/JPARC. The theoretical uncertainties of branching ratios within the SM are well under control. In the B sector, it is tentative to explain the B-meson anomalies RD(∗) and/or RK(∗) by effects of physics beyond the SM. Although NP seems to be present in the third fermion generation it might also manifest in the flavor changing neutral current transition s→d. Together with the anticipated good experimental sensitivities and accurate theoretical predictions for K→πνν¯, this motivates studies of correlated effects of NP in rare K→πνν¯ and B→K(∗)μ+μ- decays. Here we consider the loop induced effects in K→πνν¯ in two leptoquark models designed to address lepton-flavor universality violation in the RK(∗) anomalies.