Palatable Leptoquark Scenarios for Lepton Flavor Violation in Exclusive $b\to s\ell_1\ell_2$ modes

We examine various scenarios that involve a light ${\cal O}(1 TeV)$ leptoquark state and select those which are compatible with the current experimental values for $\mathcal{B}(B_s\to \mu\mu)$, $\mathcal{B}(B\to K\mu\mu)_{\mathrm{large}-q^2}$, $R_K=\mathcal{B^\prime}(B\to K\mu\mu)/\mathcal{B^\prime}(B\to Kee)$, and which lead to predictions consistent with other experimental data. We show that two such scenarios are phenomenologically plausible, namely the one with a doublet of scalar leptoquarks of hypercharge $1/6$, and the one with a triplet of vector leptoquarks of hypercharge $2/3$. We also argue that a model with a singlet scalar leptoquark of hypercharge $1/3$ is not viable. Using the present experimental data as constraints, it is shown that the exclusive lepton flavor violating decays, $\mathcal{B}(B_s\to \mu\tau)$, $\mathcal{B}(B\to K \mu\tau)$ and $\mathcal{B}(B\to K^\ast \mu\tau)$, can be as large as $\mathcal{O}(10^{-5})$.