Abstract
We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B6 (1/2) and B8 (3/2) parametrizing the K → ππ matrix elements 〈Q6〉0 and 〈Q8〉2 of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B6 (1/2) ≤ B8 (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 Qi contributing to the K → ππ amplitudes A0 and A2, obtained by this lattice collaboration, provides further support to our large N approach. In particular, the lattice result for the matrix element 〈Q8〉0 implies for the corresponding parameter B8 (1/2) = 1.0 ± 0.2 to be compared with large N value B8 (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 B8 (3/2) from RBC-UKQCD collaboration, our upper bound on B6 (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 |
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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