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

Understand

We review and update our results for K-> pipi decays and K^0-\bar 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.