Lepton flavor (universality) violation in rare kaon decays

Recent anomalies in the decays of $B$-mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that 4-fermion operators which can explain the $B$-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on $K\to\pi\ell \ell'$ and $K\to\ell \ell'$ decays $(\ell=\mu,e)$. For these processes, we note the corresponding physics opportunities at the NA62 and KOTO experiments. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test the $B$-physics anomalies in the kaon sector.