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. . 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) similar or equal to 1 TeV can alone accommodate the above mentioned anomalies. The only single leptoquark scenario which can provide a viable solution for m(LQ) similar or equal to 1 divided by 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 bs +/- modes, such as B(BK). Improving the experimental upper bound on B(BK) by two orders of magnitude could compromise the viability of the minimal U-1 model as well.