QCD Improved Matching for Semi-Leptonic B Decays with Leptoquarks

Leptoquarks (LQs) provide very promising solutions to the tensions between the experimental measurements and the SM predictions of $b\to s\ell^+\ell^-$ and $b\to c\tau\nu$ processes. In this case the LQ masses are in general at the TeV scale and they can thus be produced at high energy colliders and dedicated LHC searches are ongoing. While for LQ production and decay the $O(\alpha_s)$ corrections have been known for a long time, the $O(\alpha_s)$ corrections to the matching on 2-quark-2-lepton operators have not been calculated, yet. In this article we close this gap by computing the QCD corrections to the matching of LQ models on the effective SM Lagrangian for both scalar and vector LQs. We find an enhancement of the Wilson coefficients of vector operators with respect to the tree-level results of around 8 % (13 %) if they originate from scalar (vector) LQs. This softens the LHC bounds and increases the allowed parameter space of LQ models addressing the flavour anomalies.