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

TL;DR

This paper derives the complete leading order and next-to-leading order QCD matching conditions for $F=2$ processes in scalar leptoquark models, refining theoretical predictions and reducing uncertainties in flavor physics constraints.

Contribution

It provides the first comprehensive calculation of NLO QCD corrections for $F=2$ processes in all scalar leptoquark representations, enhancing the precision of flavor observable predictions.

Findings

Two-loop corrections increase $F=2$ effects by 5-10%.

NLO corrections reduce matching scale uncertainties.

Complete LO matching for all scalar LQ representations.

Abstract

Leptoquarks provide viable solutions to the flavour anomalies, i.e. they can explain the tensions between the measurements and the Standard Model predictions of the anomalous magnetic moment of the muon as well as $b\to s\ell^+\ell^-$ and $b\to c\tau\nu$ processes. However, leptoquarks also contribute to other flavour observables, such as $\Delta F=2$ processes, at the loop-level. In particular, $B_s-\bar B_s$ mixing provides a crucial bound in setups addressing $b\to c\tau\nu$ data, often excluding a big portion of the parameter space that could otherwise account for it. In this article, we first derive the complete leading order matching, including all five scalar LQ representations, 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-leading order $\alpha_s$ matching corrections to these $\Delta F=2$ processes in generic scalar leptoquark models. We find that the two-loop corrections increase the effects in $\Delta F=2$ processes by $\sim 5$-$10\%$ and significantly reduce the matching scale uncertainty.