## Abstract

We calculate BSM hadronic matrix elements for K ^{0} –K ^{¯ 0} mixing in the Dual QCD approach (DQCD). The ETM, SWME and RBC-UKQCD lattice collaborations find the matrix elements of the BSM density–density operators O _{i} with i = 2–5 to be rather different from their vacuum insertion values (VIA) with B _{2} ≈ 0.5, B _{3} ≈ B _{5} ≈ 0.7 and B _{4} ≈ 0.9 at µ = 3 GeV to be compared with B _{i} = 1 in the VIA. We demonstrate that this pattern can be reconstructed within the DQCD through the non-perturbative meson evolution from very low scales, where factorization of matrix elements is valid, to scales O(1 GeV) with subsequent perturbative quark–gluon evolution to µ = 3 GeV. This turns out to be possible in spite of a very different pattern displayed at low scales with B _{2} = 1.2, B _{3} = 3.0, B _{4} = 1.0 and B _{5} ≈ 0.2 in the large-N limit, N being the number of colours. Our results imply that the inclusion of meson evolution in the phenomenology of any non-leptonic transition like K ^{0} –K ^{¯ 0} mixing and K → ππ decays is mandatory. While meson evolution, as demonstrated in our paper, is hidden in lattice QCD results, to our knowledge, DQCD is the only analytic approach for non-leptonic transitions and decays which takes this important strong dynamics into account.

Original language | English |
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Pages (from-to) | 121-140 |

Number of pages | 20 |

Journal | Acta Physica Polonica B |

Volume | 50 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2019 |

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