Anomalous Form Factor of the Neutral Pion in Extended AdS/QCD Model with Chern-Simons Term

TL;DR

This paper extends the AdS/QCD model by adding a Chern-Simons term to accurately reproduce the chiral anomaly and studies the pion-photon vertex function, finding results consistent with experimental data and perturbative QCD.

Contribution

It introduces a Chern-Simons term into the hard-wall AdS/QCD model and analyzes the resulting pion-photon form factor, including its asymptotic behavior and VMD structure.

Findings

Slope of the form factor matches experimental data.

Model's large virtuality limit agrees with perturbative QCD.

Predictions include nontrivial dependence on photon virtuality ratio.

Abstract

We propose an extension of the hard-wall AdS/QCD model by including the Chern-Simons term required to reproduce the chiral anomaly of QCD. In the framework of this holographic model, we study the vertex function F_{\pi \gamma^* \gamma^*}(Q_1^2,Q_2^2) which accumulates information about the coupling of the pion to two (in general virtual) photons. We calculate the slope of the form factor with one real and one slightly virtual photon and show that it is close to experimental findings. We analyze the formal limit of large virtualities and establish that predictions of the holographic model analytically (including nontrivial dependence on the ratio of photon virtualities) coincide with those of perturbative QCD with asymptotic pion distribution amplitude. We also investigate the generalized VMD structure of F_{\pi \gamma^* \gamma^*}(Q_1^2,Q_2^2) in the extended AdS/QCD model.