Closing the window on single leptoquark solutions to the B-physics anomalies

We examine various scenarios in which the Standard Model is extended by a light leptoquark state to solve for one or both B-physics anomalies, viz. R_D(*)ᵉˣᵖ>R_D(*)SM R D * exp > R D * S M or/and R_K(*)ᵉˣᵖ>R_K(*)SM R K * exp > R K * S M . To do so we combine the constraints arising both from the low-energy observables and from direct searches at the LHC. We find that none of the scalar leptoquarks of mass m LQ ≃ 1 TeV can alone accommodate the above mentioned anomalies. The only single leptoquark scenario which can provide a viable solution for m LQ ≃ 1÷2 TeV is a vector leptoquark, known as U 1, which we re-examine in its minimal form (letting only left-handed couplings to have non-zero values). We find that the limits deduced from direct searches are complementary to the low-energy physics constraints. In particular, we find a rather stable lower bound on the lepton flavor violating b → sℓ 1 ± ℓ 2 ∓ modes, such as ℬ(B → Kμτ). Improving the experimental upper bound on ℬ(B → Kμτ) by two orders of magnitude could compromise the viability of the minimal U 1 model as well.