## Abstract

I summarize the status of the δ I = 1/2 rule in K → ππ decays within an analytic approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N, where N is the number of colours. This approximate approach, developed in the 1980s by William Bardeen, Jean-Marc Gérard and myself, allowed us already 28 years ago to identify the dominant dynamics behind the δ I = 1/2 rule. However, the recent inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones to hadronic matrix elements of current-current operators and the calculation of the corresponding Wilson coefficients in a momentum scheme at the NLO improved significantly the matching between quark-gluon short distance contributions and meson long distance contributions over our results in 1986. We obtain satisfactory description of the ReA_{2} amplitude and ReA_{0}/ReA_{2} = 16.0 ± 1.5 to be compared with its experimental value of 22.3. While this difference could be the result of present theoretical uncertainties in our approach, it cannot be excluded that New Physics (NP) is here at work. The analysis by Fulvia De Fazio, Jennifer Girrbach-Noe and myself shows that indeed a tree-level Z′ or G′ exchanges with masses in the reach of the LHC and special couplings to quarks can significantly improve the theoretical status of the δ I = 1/2 rule while satisfying constraints from ε_{K}, ε′/ε, δ M_{K}, LEP-II and the LHC. The ratio ε′/ε plays an important role in these considerations. I stress that our approach allows to understand the physics behind recent numerical results obtained in lattice QCD not only for the δ I = 1/2 rule but also for the parameter B_{K} that enters the evaluation of ε_{K}. In contrast to the δ I = 1/2 rule and ε′/ε the chapter on B_{K} in QCD appears to be basically closed.

Originalsprache | Englisch |
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Titel | EPJ Web of Conferences |

Redakteure/-innen | Claudio Coriano, Pietro Colangelo, Donato Creanza, Eugenio Nappi, Fulvia De Fazio, Giuseppe E. Bruno, Gabriele Chiodini |

Herausgeber (Verlag) | EDP Sciences |

ISBN (elektronisch) | 9782759816859 |

DOIs | |

Publikationsstatus | Veröffentlicht - 2014 |

Veranstaltung | 2014 7th International Workshop on Quantum Chromodynamics - Theory and Experiment, QCD@Work 2014 - Giovinazzo, Bari, Italien Dauer: 16 Juni 2014 → 19 Juni 2014 |

### Publikationsreihe

Name | EPJ Web of Conferences |
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Band | 80 |

ISSN (Print) | 2101-6275 |

ISSN (elektronisch) | 2100-014X |

### Konferenz

Konferenz | 2014 7th International Workshop on Quantum Chromodynamics - Theory and Experiment, QCD@Work 2014 |
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Land/Gebiet | Italien |

Ort | Giovinazzo, Bari |

Zeitraum | 16/06/14 → 19/06/14 |

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