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

Abstract

Rare $K\to \pi \nu \bar{\nu }$ decays, being dominated by short distance contributions within the Standard Model (SM), open a window for New Physics (NP) searches at low energies. The $K\to \pi \nu \bar{\nu }$ branching ratios are expected to be measured with $\sim 10\%$ 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 $R_{D^{(\ast )}}$ and/or $R_{K^{(\ast )}}$ 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 $s\to d$. Together with the anticipated good experimental sensitivities 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 $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$ decays. Here we consider the loop induced effects in $K\to \pi \nu \bar{\nu }$ in two leptoquark models designed to address lepton-flavor universality violation in the $R_{K^{(\ast )}}$ anomalies.