$\epsilon^\prime/\epsilon$-2018: A Christmas Story

TL;DR

This paper discusses the status of the $psilon'/psilon$ ratio, arguing for evidence of new physics beyond the Standard Model based on dual QCD approach and criticizing other methods' conclusions.

Contribution

It presents a novel argument for the presence of new physics in $psilon'/psilon$ using the dual QCD approach and critiques existing lattice QCD and chiral perturbation theory results.

Findings

Dual QCD predicts $psilon'/psilon$ below experimental data without new physics.

Inclusion of pion loops alone does not reconcile theory with experiment.

Future lattice QCD results may reveal signs of new physics in $psilon'/psilon$.

Abstract

I was supposed to review the status of $\epsilon^\prime/\epsilon$ both at the CKM Workshop in September in Heidelberg and recently at the Discrete 2018 Conference in Vienna. Unfortunately I had to cancel both talks for family reasons. My main goal in these talks was to congratulate NA48 and KTeV collaborations for the discovery of new sources of CP violation through their heroic efforts to measure the ratio $\epsilon^\prime/\epsilon$ in the 1980s and 1990s with final results presented roughly 16 years ago. As I will not attend any other conferences this year I will reach this goal in this writing. In this context I will give arguments, why I am convinced about the presence of new physics in $\epsilon^\prime/\epsilon$ on the basis of my work with Jean-Marc Gerard within the context of the Dual QCD (DQCD) approach and why RBC-UKQCD collaboration and in particular Chiral Perturbation Theory practitioners are still unable to reach this conclusion. I will demonstrate that even in the presence of pion loops, as large as advocated recently by Gilbert and Pich, the value of $\epsilon^\prime/\epsilon$ is significantly below the data, when the main non-factorizable QCD dynamics at long distance scales, represented in DQCD by {the meson evolution}, is taken into account. As appriopriate for a Christmas story, I will prophesy the final value of $\epsilon^\prime/\epsilon$ within the SM, which should include in addition to the correct matching between long and short distance contributions, isospin breaking effects, NNLO QCD corrections to both QCD penguin and electroweak penguin contributions and final state interactions. Such final SM result will probably be known from lattice QCD only in the middle of 2020s, but already in 2019 we should be able to see some signs of NP in the next result on $\epsilon^\prime/\epsilon$ from RBC-UKQCD.