SVZ + 1/q2 expansion versus some QCD holographic Models

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.