SVZ + 1/q2 expansion versus some QCD holographic Models

TL;DR

This paper compares SVZ + 1/q^2 expansion results with QCD holographic models for two-point correlators, revealing that certain holographic models naturally incorporate the 1/q^2 term and can semi-quantitatively reproduce condensate contributions.

Contribution

It demonstrates the natural emergence of the 1/q^2 term in holographic models and relates the dilaton parameter to the tachyonic gluon mass, providing a bridge between phenomenology and holographic QCD.

Findings

The 1/q^2 term appears naturally in MSW and GSD models.

Hard-Wall model deviates significantly due to lack of power corrections.

Holographic models require a tachyonic gluon mass of about -(0.12-0.14) GeV^2.

Abstract

Considering the classical two-point correlators built from (axial)-vector, scalar \bar qq and gluonium currents, we confront results obtained using the SVZ + 1/q^2 expansion to the ones from some QCD holographic models in the Euclidian region and with negative dilaton \Phi_i(z)=- |c_i^2| z^2. We conclude that the presence of the 1/q^2-term in the SVZ-expansion due to a tachyonic gluon mass appears naturally in the Minimum Soft Wall (MSW) and the Gauge/String Dual (GSD) models which can also reproduce semi-quantitatively some of the higher dimension condensate contributions appearing in the OPE. The Hard-Wall model shows a large departure from the SVZ + 1/q^2 expansion in the vector, scalar and gluonium channels due to the absence of any power corrections. The equivalence of the MSW and GSD models is manifest in the vector channel through the relation of the dilaton parameter with the tachyonic gluon mass. For approximately reproducing the phenomenological values of the dimension d=4,6 condensates, the holographic models require a tachyonic gluon mass (\alpha_s/\pi)\lambda^2= -(0.12- 0.14) GeV^2, which is about twice the fitted phenomenological value from e^+e^- data. The relation of the inverse length parameter c_i to the tachyonic gluon mass also shows that c_i is channel dependent but not universal for a given holographic model. Using the MSW model and M_\rho=0.78 GeV as input, we predict a scalar \bar qq mass M_S=(0.95-1.10) GeV and a scalar gluonium mass M_G= (1.1- 1.3) GeV.