$\pi^0, \eta, \eta^\prime$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2)_\mu$

TL;DR

This paper calculates the two-photon transition form factors of light pseudoscalar mesons using a holographic QCD model and assesses their impact on the muon's anomalous magnetic moment.

Contribution

It introduces a holographic soft-wall model solution for the $U(1)_A$ problem to compute meson transition form factors and compares them with experimental data.

Findings

Transition form factors agree with experimental data across photon virtualities.

Form factors contribute to the hadronic light-by-light scattering in muon g-2 calculations.

Provides a holographic QCD approach to meson-photon interactions.

Abstract

We compute the two-photon transition form factors of the light pseudoscalar $\pi^0$, $\eta$ and $\eta^\prime$ mesons in a soft-wall holographic model of QCD with a solution of the $U(1)_A$ problem. We compare the results with the experimental data in different ranges of photon virtualities. The obtained transition form factors are used to determine the $\pi^0$, $\eta$ and $\eta^\prime$ pole terms in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.