Pion form factor from an AdS deformed background

TL;DR

This paper develops a bottom-up AdS/QCD model with an exponential deformation to study the pion form factor, achieving good agreement with experimental data, especially when considering a momentum-dependent infrared scale.

Contribution

It introduces a deformed AdS background with a conformal exponential factor to model pion properties and compares different infrared scale assumptions.

Findings

Momentum-dependent infrared scale yields better experimental agreement.

The model accurately reproduces the pion form factor and radius.

Comparison with other models validates the approach.

Abstract

We consider a bottom-up AdS/QCD model with a conformal exponential deformation $e^{k\,z^2}$ on a Lorentz invariant AdS background. In this model, we assume the conformal dimension associated with the operator that creates pions at the boundary as $\Delta=3$. Regarding the infrared scale related to photon field $k_\gamma$, we analyze two cases: constant and depending on the transferred momentum $q$. In these two cases, we computed the electromagnetic pion form factor as well as the pion radius. We compare our results with experimental data as well as other theoretical (holographic and non-holographic) models. In particular, for the momentum-dependent infrared scale, we find good agreement with the available experimental data as well as non-holographic models.