Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory

TL;DR

This paper modifies a holographic QCD model to correctly reproduce the operator product expansion and chiral parameters, linking Regge trajectories with QCD Green functions and chiral symmetry breaking.

Contribution

It introduces a modified dilaton potential in the soft wall model to align the OPE with QCD and analytically describes low-energy chiral parameters.

Findings

OPE is recovered with a boundary term and condensates

Chiral parameters $F_\pi$ and $L_{10}$ are accurately modeled

The model supports the use of Digamma functions for QCD Green functions

Abstract

The soft wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply OPE. We study also the axial two-point function using the same modified dilaton field and an additional scalar field to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, $F_\pi$ and $L_{10}$, are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.