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Large N Approach to Kaon Decays and Mixing 28 Years Later: Delta I = 1/2 Rule, hat B_K and Delta M_K

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Buras, Andrzej J. [TUM-IAS, Munich] Gérard, Jean-Marc [UCL] Bardeen, William A. [Fermilab]

We review and update our results for K-> pipi decays and K^0-ar 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 Delta I = 1/2 rule for K-> pi pi 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 uniquely from our analytic approach. At NLO in 1/N we obtain ReA_0/ReA_2= 16.0pm 1.5 which amounts to an order of magnitude enhancement over the strict large N limit value sqrt{2}. QCD penguins contribute at 15% level to this result. We also find hat B_K=0.73pm 0.02, with the smallness of 1/N corrections to the large N value hat 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 Delta M_K in this approach.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2014
Language Anglais
Journal information "European Physical Journal C. Particles and Fields" - Vol. 74, no.5, p. 2871 (2014)
Peer reviewed yes
Publisher Springer ((Germany) Heidelberg)
issn 1434-6044
e-issn 1434-6052
Publication status Publié
Affiliations UCL - SST/IRMP - Institut de recherche en mathématique et physique
UCL - (SLuc) Service d'oto-rhino-laryngologie
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Bibliographic reference Buras, Andrzej J. ; Gérard, Jean-Marc ; Bardeen, William A.. Large N Approach to Kaon Decays and Mixing 28 Years Later: Delta I = 1/2 Rule, hat B_K and Delta M_K. In: European Physical Journal C. Particles and Fields, Vol. 74, no.5, p. 2871 (2014)
Permanent URL http://hdl.handle.net/2078.1/152761