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

Abstract

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. $R_{D^{(\ast )}}^{\exp }>R_{D^{(\ast )}}^{\mathrm{SM}}$ or/and $R_{K^{(\ast )}}^{\exp }<R_{K^{(\ast )}}^{\mathrm{SM}}$. 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 $m_{\mathrm{LQ}}\simeq 1$ TeV can alone accommodate the above mentioned anomalies. The only single leptoquark scenario which can provide a viable solution for $m_{\mathrm{LQ}}\simeq 1÷2$ 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 $b\to s{\ell }_1^{\pm }{\ell }_2^{\mp }$ modes, such as $\mathcal{B}(B\to K\mu \tau )$. Improving the experimental upper bound on $\mathcal{B}(B\to K\mu \tau )$ by two orders of magnitude could compromise the viability of the minimal $U_1$ model as well.

Comments: 33 pages, 10 figures; v3: Version to appear in JHEP