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Leptoquarks provide viable solutions to the flavour anomalies, i.e. they canexplain the tensions between the measurements and the Standard Modelpredictions of the anomalous magnetic moment of the muon as well as $b\tos\ell^+\ell^-$ and $b\to c\tau\nu$ processes. However, leptoquarks alsocontribute to other flavour observables, such as $\Delta F=2$ processes, at theloop-level. In particular, $B_s-\bar B_s$ mixing provides a crucial bound insetups addressing $b\to c\tau\nu$ data, often excluding a big portion of theparameter space that could otherwise account for it. In this article, we firstderive the complete leading order matching, including all five scalar LQrepresentations, for $D^0-\bar D^0$, $K^0-\bar K^0$ and $B_{s,d}-\bar B_{s,d}$mixing (at the dimension-six level). We then calculate the next-to-leadingorder $\alpha_s$ matching corrections to these $\Delta F=2$ processes ingeneric scalar leptoquark models. We find that the two-loop correctionsincrease the effects in $\Delta F=2$ processes by $\sim 5$-$10\%$ andsignificantly reduce the matching scale uncertainty.

Next-to-Leading-Order QCD Matching for $\Delta F=2$ Processes in Scalar Leptoquark Models