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.

Comments: 8 pages, Proceedings of the Kaon 2016 Conference