## Abstract

We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B_{6} ^{(1/2)} and B_{8} ^{(3/2)} parametrizing the K → ππ matrix elements 〈Q_{6}〉_{0} and 〈Q_{8}〉_{2} of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B_{6} ^{(1/2)} ≤ B_{8} ^{(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 Q_{i} contributing to the K → ππ amplitudes A_{0} and A_{2}, obtained by this lattice collaboration, provides further support to our large N approach. In particular, the lattice result for the matrix element 〈Q_{8}〉_{0} implies for the corresponding parameter B_{8} ^{(1/2)} = 1.0 ± 0.2 to be compared with large N value B_{8} ^{(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 B_{8} ^{(3/2)} from RBC-UKQCD collaboration, our upper bound on B_{6} ^{(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 language | English |
---|---|

Article number | 8 |

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 12 |

DOIs | |

State | Published - 1 Dec 2015 |

## Keywords

- CP violation
- Kaon Physics

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