Upper bounds on ε′/ε parameters B6(1/2) and B8(3/2) from large N QCD and other news

Andrzej J. Buras, Jean Marc Gérard

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Abstract

We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B6 (1/2) and B8 (3/2) parametrizing the K → ππ matrix elements 〈Q60 and 〈Q82 of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B6 (1/2) ≤ B8 (3/2) < 1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Qi contributing to the K → ππ amplitudes A0 and A2, obtained by this lattice collaboration, provides further support to our large N approach. In particular, the lattice result for the matrix element 〈Q80 implies for the corresponding parameter B8 (1/2) = 1.0 ± 0.2 to be compared with large N value B8 (1/2) = 1.1 ± 0.1. We discuss briefly the implications of these findings for the ratio ε′/ε. In fact, with the precise value for B8 (3/2) from RBC-UKQCD collaboration, our upper bound on B6 (1/2) implies ε′/ε in the SM roughly by a factor of two below its experimental value (16.6± 2.3) × 10−4. We also briefly comment on the parameter B^K$$ {\widehat{B}}_K $$ and the ΔI = 1/2 rule.

Original languageEnglish
Article number8
Pages (from-to)1-20
Number of pages20
JournalJournal of High Energy Physics
Volume2015
Issue number12
DOIs
StatePublished - 1 Dec 2015

Keywords

  • CP violation
  • Kaon Physics

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