A holographic approach to low-energy weak interactions of hadrons

Abstract

We apply the double-trace formalism to incorporate nonleptonic weak interactions of hadrons into holographic models of the strong interactions. We focus our attention upon $\Delta S=1$ nonleptonic kaon decays. By working with a Yang-Mills--Chern-Simons 5-dimensional action, we explicitly show how, at low energies, one recovers the $\Delta S=1$ weak chiral Lagrangian for both the anomalous and nonanomalous sectors. We provide definite predictions for the low energy coefficients in terms of the AdS metric and argue that the double-trace formalism is a 5-dimensional avatar of the Weak Deformation Model introduced long ago by Ecker et al. As a significant phenomenological application, we reassess the $K\to 3\pi$ decays in the light of the holographic model. Previous models found a fine-tuned cancellation of resonance exchange in these decays, which was both conceptually puzzling and quantitatively in disagreement with experimental results. The holographic model we build is an illustrative counterexample showing that the cancellation encountered in the literature is not generic but a model-dependent statement and that agreement with experiment can be obtained.