Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$

Abstract

The quantity ${\epsilon }^{\prime }/\epsilon$ measures direct CP violation in Kaon decays. Recent SM predictions show a $2.9\sigma$ tension with data, with the theoretical uncertainty dominating. As rapid progress on the lattice is bringing nonperturbative long-distance effects under control, a more precise knowledge of short-distance contributions is needed. We describe the first NNLO results for ${\epsilon }^{\prime }/\epsilon$ and discuss future prospects, as well as issues of scheme dependence and the separation of perturbative and nonperturbative effects. Finally we also comment on the solution of the renormalisation-group evolution in one of the talks at this conference and present the correct solution.

arXiv comment8 pages, Proceedings of the Kaon 2016 Conference

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Cited by in corpus (16)

• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• 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
• Anatomy of ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• $K\to \pi \nu \overline{\nu }$ in the MSSM in Light of the ${\epsilon }_K^{\prime }/{\epsilon }_K$ Anomaly
• ${\epsilon }^{\prime }/\epsilon$ in the Standard Model at the Dawn of the 2020s
• BSM Hadronic Matrix Elements for ${\epsilon }^{\prime }/\epsilon$ and $K\to \pi \pi$ Decays in the Dual QCD Approach
• $K\to \pi \pi$ and $K-\pi$ Matrix Elements of the Chromomagnetic Operators from Dual QCD
• Isospin-breaking in ${\epsilon }^{\prime }/\epsilon$: Impact of ${\eta }_0$ at the Dawn of the 2020s
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• The Dual QCD @ Work
• Kaon physics overview
• General non-leptonic $\Delta F=1$ WET at the NLO in QCD
• The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ in the SM: 2019