Abstract
We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B (1/2)6 and B (3/2)8 parametrizing the K → ππ matrix elements 〈Q 6〉0 and 〈Q 8〉2 of the dominant QCD and electroweak operators receive both negative \( \mathcal{O}\left(1/N\right) \) corrections such that B (1/2)6 ≤ B (3/2)8 < 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 (1/2)8 = 1.0 ± 0.2 to be compared with large N value B (1/2)8 = 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 (3/2)8 from RBC-UKQCD collaboration, our upper bound on B (1/2)6 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 \( {\widehat{B}}_K \) and the ΔI = 1/2 rule.
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Buras, A.J., Gérard, JM. Upper bounds on ε′/ε parameters B (1/2)6 and B (3/2)8 from large N QCD and other news. J. High Energ. Phys. 2015, 1–20 (2015). https://doi.org/10.1007/JHEP12(2015)008
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DOI: https://doi.org/10.1007/JHEP12(2015)008