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arXiv · 2107.10262

General non-leptonic $\Delta F=1$ WET at the NLO in QCD

Jason Aebischer·Christoph Bobeth·Andrzej J. Buras·Jacky Kumar·Mikołaj Misiak
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Abstract

We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic $\Delta F=1$ decays that govern $s\to d$ and $b\to d, s$ transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers $N_f$ of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of $K\to\pi\pi$ and non-leptonic $B$-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

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Jason Aebischer, Christoph Bobeth, Andrzej J. Buras, Jacky Kumar, Mikołaj Misiak. 2021-07-21. General non-leptonic $\Delta F=1$ WET at the NLO in QCD. https://doi.org/10.1007/jhep11(2021)227

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