Anomalous $AV^*V$ vertex function in the soft-wall holographic model of QCD

TL;DR

This paper investigates the $AV^*V$ vertex function within the soft-wall holographic QCD model, comparing its predictions for structure functions and correlation functions to known QCD results, revealing both consistencies and discrepancies.

Contribution

It introduces the calculation of the $AV^*V$ vertex functions in the soft-wall holographic model and compares these to QCD, highlighting anomalous features and low-energy constants.

Findings

The computed $w_L$ and $w_T$ functions show partial agreement with QCD results.

The two-point correlation functions are close to QCD predictions.

The model reveals anomalous behavior in the vertex function.

Abstract

We consider the vertex function of two vector and one axial-vector currents using the soft-wall holographic model of QCD with the Chern-Simons term. Two structure functions $w_L$ and $w_T$ describe such a vertex in the special case in which one of the two vector currents corresponds to an on-shell soft photon. We briefly review the QCD results for these functions, obtained from triangular loop diagrams with quarks having mass $m_q=0$ or $m_q \neq 0$, we compute $w_L$ and $w_T$ in the soft-wall model and compare the outcome to the QCD findings. We also calculate and discuss the two-point $\Pi_{VV}-\Pi_{AA}$ correlation function, together with a few low-energy constants, which turn out to be close to the QCD results.