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

2014/01/07 by Andrzej J. Buras, Buras, Andrzej J., Jean‐Marc Gérard +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1401.1385

openalex publication_date 2014/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review and update our results for K-> pipi decays and K⁰- K⁰ mixing\nobtained by us in the 1980s within an approach based on the dual representation\nof QCD as a theory of weakly interacting mesons for large N colours. In our\nanalytic approach the dynamics behind the enhancement of ReA₀ and suppression\nof ReA₂, the so-called Delta I = 1/2 rule for K-> pi pi decays, has a simple\nstructure: the usual octet enhancement through quark-gluon renormalization\ngroup evolution down to the scales O(1 GeV) is continued as a meson evolution\ndown to zero momentum scales at which the factorization of hadronic matrix\nelements is at work. The inclusion of lowest-lying vector meson contributions\nin addition to the pseudoscalar ones and of Wilson coefficients in a momentum\nscheme improves significantly the matching between quark-gluon and meson\nevolutions. In particular, the anomalous dimension matrix governing the meson\nevolution exhibits the structure of the known anomalous dimension matrix in the\nquark-gluon evolution. The recent results on ReA₂ and ReA₀ from the RBC-UKQC\ncollaboration give support for our approach. In particular, the signs of the\ntwo main contractions found numerically by these authors follow uniquely from\nour analytic approach. At NLO in 1/N we obtain ReA₀/ReA₂= 16.0\± 1.5 which\namounts to an order of magnitude enhancement over the strict large N limit\nvalue sqrt2. QCD penguins contribute at 15% level to this result. We also\nfind B_K=0.73\± 0.02, with the smallness of 1/N corrections to the large\nN value B_K=3/4 resulting within our approach from an approximate\ncancellation between pseudoscalar and vector meson one-loop contributions. We\nsummarize the status of Delta M_K in this approach.\n

Citations

• Hyperons and Heavy Mesons (Systematics and Decay)
• Emerging Understanding of theΔI=1/2Rule from Lattice QCD

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