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Title: Large $N$ approach to kaon decays and mixing 28 years later: $$\Delta I = 1/2$$ rule, $$\hat B_K$$ and $$\Delta M_K$$

We review and update our results for K → π π decays and K⁰- K¯⁰ mixing obtained by us in the 1980s within an approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N colours. In our analytic approach the dynamics behind the enhancement of ReA 0 and suppression of ReA 2, the so-called ΔI = 1/2 rule for K → π π decays, has a simple structure: the usual octet enhancement through quark-gluon renormalization group evolution down to the scales O(1 GeV) is continued as a meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark-gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark-gluon evolution. The recent results on ReA 2 and ReA 0 from the RBC-UKQC collaboration give support for our approach. In particular, the signs of the two main contractions found numerically by these authors follow uniquelymore » from our analytic approach. At NLO in 1/N we obtain R = ReA 0/ReA 2= 16.0±1.5 which amounts to an order of magnitude enhancement over the strict large N limit value √2. QCD penguins contribute at 15% level to this result. We also find B^ K = 0.73± 0.02, with the smallness of 1/N corrections to the large N value B^ K = 3/4 resulting within our approach from an approximate cancellation between pseudoscalar and vector meson one-loop contributions. We summarize the status of ΔM K in this approach.« less
 [1] ;  [2] ;  [3]
  1. TUM Institute for Advanced Study, Garching (Germany); Technische Univ. Munchen, Garching (Germany)
  2. Univ. catholique de Louvain, Louvain-la-Neuve (Belgium)
  3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1434-6044; arXiv eprint number arXiv:1401.1385
Grant/Contract Number:
Accepted Manuscript
Journal Name:
European Physical Journal. C, Particles and Fields
Additional Journal Information:
Journal Volume: 74; Journal Issue: 5; Journal ID: ISSN 1434-6044
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
OSTI Identifier: