Glueball-Meson Mixing In Holographic QCD

TL;DR

This paper investigates glueball-meson mixing in holographic QCD using the Witten-Sakai-Sugimoto model, incorporating backreaction effects to improve the accuracy of mass spectrum predictions.

Contribution

It introduces a method to include finite Nf/Nc effects and backreaction in holographic QCD, deriving corrected mass spectra and a technique for analyzing vector-scalar mixing.

Findings

Derived a corrected effective action for glueball and meson states.

Calculated first-order mass corrections showing significant mixing effects.

Developed a numerical technique for eigenstate determination in mixed Lagrangians.

Abstract

Top-down holographic QCD models often work in the "probe" (or "quenched") limit, which assumes that the number of colors is much greater than the number of flavors. Relaxing this limit is essential to a fuller understanding of holography and more accurate phenomenological predictions. In this work, we focus on a mixing of glueball and meson mass eigenstates that arises from the DBI action as a finite Nf/Nc effect. For concreteness, we work in the Witten-Sakai-Sugimoto model, and show that this mixing must be treated in conjunction with the backreaction of the flavor branes onto the background geometry. Including the backreaction with the simplification that it is "smeared out" over the compact transverse direction, we derive a corrected effective action for the vector glueball and scalar states. Along the way, we observe a Stueckelberg-like mechanism that restores translation invariance in the transverse direction. We also derive a general technique, that lends itself easily to numerics, for finding mass eigenstates of Lagrangians with vector-scalar mixing. We then calculate the first order corrections to the mass spectra of both the vector and scalar particles, and show that the term that explicitly mixes vector and scalar states is the most significant correction to the masses of low-lying scalar mesons.