Abstract
The soft wall model in holographic QCD has Regge trajectories but wrong oper- ator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply with the OPE. We study also the axial two-point function us- ing the same modified dilaton field and an additional scalar fie ld to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, Fπ and L10, are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocat- ing Digamma function to study QCD two-point functions in different momentum regions.
Highlights
QCD Green functions describe three ranges of energies (i) deep euclidean, where perturbative QCD and operator product expansion (OPE) expansion methods can be applied, (ii) an intermediate Minkowski region, where resonances are described by Regge trajectories and (iii) the strong interacting, low-energy region, described by chiral perturbation theory (χ PT) [1]
Low energy QCD properties, like the chiral symmetry breaking (χ SB) parameters, Fπ and the Gasser-Leutwyler coefficients Li ’s of the O( p4) chiral Lagrangian have been studied in the framework of holographic models of QCD, based on the AdS/CFT correspondence [9,10,11]
We shall assume that the effects of the OPE on the vector current two-point functions in QCD can be encoded in a new profile for the dilaton field of the Soft Wall model (SW) model
Summary
QCD Green functions describe three ranges of energies (i) deep euclidean, where perturbative QCD and OPE expansion methods can be applied, (ii) an intermediate Minkowski region, where resonances are described by Regge trajectories and (iii) the strong interacting, low-energy region, described by chiral perturbation theory (χ PT) [1]. In order to reproduce resonances masses with a Regge spacing, one can consider a 5D model with AdS metric and an additional field, the dilaton [20] In this model it can be shown that the partonic log of the two point vectorial Green function. This will be exactly our starting point: OPE tells us the correct Green functions in the deep Euclidean in terms of gluon and quarks condensates Is it possible to modify the dilaton profile, φ(z) → φ(z) + δφ(z), such to comply with QCD requirements in the intermediate (Regge) region and UV (OPE) region? Implementing the correct OPE and mass spectrum for the axial sector, we will propose our post-diction of Fπ and L10 [one of the the chiral O( p4) coefficients] in terms of our input parameters, i.e. the Regge spacing and the QCD condensates.
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