### Abstract

We present new results for the matrix elements of the Q6 and Q4 penguin operators, evaluated in a large-Nc approach which incorporates important O(Nc2nf/Nc) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as MS. Numerically, we find that there is a large positive contribution to the ΔI = 1/2 matrix element of Q6 and hence to the direct CP-violation parameter ∈′/∈. We also present results for the ΔI = 1/2 rule in K → ππ amplitudes, which incorporate the related and important "eye-diagram" contributions of O(N c21/NC) from the Q2 operator (i.e. the penguin-like contraction). The results lead to an enhancement of the ΔI = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem. © SISSA/ISAS 2003.

Original language | English |
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Pages (from-to) | 587-616 |

Journal | Journal of High Energy Physics |

Volume | 7 |

Issue number | 5 |

Publication status | Published - 1 May 2003 |

### Keywords

- 1/N Expansion
- Chiral Lagrangians
- Kaon Physics
- QCD

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## Cite this

Hambye, T., Peris, S., & De Rafael, E. (2003). Δ = 1/2 and ∈′/∈ in large-N<inf>c</inf> QCD.

*Journal of High Energy Physics*,*7*(5), 587-616.