$ε^\prime/ε$-2018: A Christmas Story

Abstract

I was supposed to review the status of ε /ε 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 ε /ε 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 ε /ε on the basis of my work with Jean-Marc Gérard within the context of the Dual QCD (DQCD) approach and why RBC-UKQCD lattice QCD 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 Gisbert and Pich, the value of ε /ε 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 appropriate for a Christmas story, I will prophesy the final value of ε /ε 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 the 2020s, but already in 2019 we should be able to see some signs of NP in the next result on ε /ε from RBC-UKQCD. In this presentation I try to avoid, as much as possible, the overlap with my recent review of Dual QCD in [1].

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

“…3 In the third column of Table I we report the results obtained with the Dual QCD (DQCD) approach [68] (for a recent summary and references see Ref. [36]). A rescaling factor of 3/2 has been applied in order to normalize the DQCD results to the amplitudes defined in Eq.…”

“…As we shall see, the phase and flavor structure of the LRSM tightly correlates nEDM, ε and ε , calling for a detailed study. We shall not enter here the debate on the SM calculations of ε that presently suffer from large uncertainties and leave open the possibility of large new physics contributions [35,36]. Our analysis will address the different scenarios according to the relevance of the LRSM contributions, addressing the present and future implications.…”

Simultaneous explanation of $K$ and $B$ anomalies in vectorlike compositeness

“…On the other hand in the Kaon sector, the observable, ε ′ /ε, which measures the direct CP violation in K → ππ decays has been focused since sizable discrepancy from the experimental data [(ε ′ /ε) exp = (16.6 ± 2.3) × 10 −4 ] [ 30,31,32,33] was reported in the standard model (SM) as (ε ′ /ε) SM = (1.06 ± 5.07) × 10 −4 [34] (see also [35]) adopting the first lattice calculation result reported by RBC-UKQCD collaboration [36]. We find various studies on this subject [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]. This anomaly would suggest us another hint for surveying possibilities of physics beyond the SM through flavor physics.…”

Constraints on New Physics from $B$ mesons

“…With this picture in mind, the recent hints for a potential anomaly in ε /ε [104][105][106][107][108] is not surprising. This parameter measures direct CP-violation in K → ππ decays and is strongly suppressed in the SM not only by the CKM hierarchy, but in addition by an accidental cancellation between contributions from QCD and electroweak penguins that enter with a relative minus sign.…”