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

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.

arXiv comment36 pages, match with the published version in JHEP

References in corpus (32)

• Dimension-Six Terms in the Standard Model Lagrangian
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• A precision measurement of direct CP violation in the decay of neutral kaons into two pions
• Electromagnetic Logarithms in B -> X_s l+ l-
• Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• Gluino Contribution to Radiative B Decays: Organization of QCD Corrections and Leading Order Results
• Low-energy effective field theory below the electroweak scale: matching at one loop
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• WCxf: an exchange format for Wilson coefficients beyond the Standard Model
• |Delta F| = 1 Nonleptonic Effective Hamiltonian in a Simpler Scheme
• Anomalous Wtb coupling effects in the weak radiative B-meson decay
• Yukawa enhancement of $Z$-mediated New Physics in $\Delta S=2$ and $\Delta B=2$ Processes
• Direct CP asymmetry in $D\to {\pi }^{-}{\pi }^{+}$ and $D\to K^{-}{K}^{+}$ in QCD-based approach
• Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• Mixing and $CP$ violation in the charm system
• Anatomy of ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• New Physics in Gamma_12^s: (sbar b) (taubar tau) Operators
• Exploring $B\to \pi \pi ,\pi K$ Decays at the High-Precision Frontier
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$