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We examine various scenarios in which the Standard Model is extended by alight leptoquark state to explain one or both $B$-physics anomalies. Combininglow-energy constraints and direct searches at the LHC, we confirm that the onlysingle leptoquark model that can explain both anomalies at the same time is avector leptoquark, known as $U_1$. Focusing on $U_1$, we highlight thecomplementarity between LHC and low--energy constraints, and argue thatimproving the experimental bound on $\mathcal{B}(B\to K\mu\tau)$ by two ordersof magnitude could compromise its viability as a solution to the $B$-physicsanomalies.

Single Leptoquark Solutions to the $B$-physics Anomalies