Holographic meson decays via worldsheet instantons

TL;DR

This paper investigates meson decay mechanisms using instanton techniques in both flat space string models and the holographic Sakai-Sugimoto model, connecting flux tube splitting probabilities with QCD formulas.

Contribution

It constructs a worldsheet instanton in the holographic model that captures meson decay, extending flux tube decay analysis to a holographic context and reproducing known QCD results.

Findings

Reproduces the CNN flux tube splitting probability in flat space model.

Constructs a holographic instanton for meson decay incorporating finite size and back-reaction effects.

Shows that in the large string limit, the holographic decay probability converges to the CNN formula.

Abstract

We study meson decays using instanton methods in two string models. The first model is the old string model in flat space which combines strings and massive particles and the second is the holographic, Sakai-Sugimoto model. Using the the old string model, we reproduce the QCD formula for the probability of splitting of the QCD flux tube derived by Casher-Neuberger-Nussinov (CNN). In the holographic model we construct a string worldsheet instanton which interpolates between a single and double string configuration, which determines the decay from one to two dual mesonic particles. The resulting probability for meson decay incorporates both the effects of finite meson size as well as back-reaction of the produced quarks on the QCD flux tube. In the limit of very large strings the probability for a split reduces to the CNN formula. A byproduct of our analysis is the analysis of the moduli space of a generic double concentric Wilson loop with circles which are separated in the holographic direction of the confining background.