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Leptoquarks (LQs) provide very promising solutions to the tensions betweenthe 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 theTeV scale and they can thus be produced at high energy colliders and dedicatedLHC 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 tothe matching on 2-quark-2-lepton operators have not been calculated, yet. Inthis article we close this gap by computing the QCD corrections to the matchingof LQ models on the effective SM Lagrangian for both scalar and vector LQs. Wefind an enhancement of the Wilson coefficients of vector operators with respectto the tree-level results of around 8 % (13 %) if they originate from scalar(vector) LQs. This softens the LHC bounds and increases the allowed parameterspace of LQ models addressing the flavour anomalies.

QCD Improved Matching for Semi-Leptonic B Decays with Leptoquarks