A holographic approach to low-energy weak interactions of hadrons

TL;DR

This paper develops a holographic model incorporating weak hadronic interactions, specifically focusing on kaon decays, and demonstrates improved agreement with experimental data over previous models by avoiding fine-tuned cancellations.

Contribution

It introduces a holographic approach using double-trace formalism to model low-energy weak interactions of hadrons, providing explicit predictions for decay coefficients and revisiting $K o 3 extpi$ decays.

Findings

Reproduces the $ riangle S=1$ weak chiral Lagrangian from holography.

Shows that resonance exchange cancellations are model-dependent.

Achieves better alignment with experimental decay rates.

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.