Subleading hadronic vacuum polarization contributions to muon $g-2$: $\mu^+\mu^- \rightarrow \gamma^* \rightarrow \pi^0 \gamma^*$

TL;DR

This paper evaluates the subleading hadronic vacuum polarization effects, involving the $a0\u03b3^*a0$ transition form factor, on the muon $g-2$, using various theoretical models fitted to experimental data.

Contribution

It introduces a comprehensive analysis of the subleading hadronic vacuum polarization contributions to muon $g-2$ using multiple models including holographic approaches.

Findings

Model predictions are significantly smaller than dispersion relation estimates.

Different form factor models yield consistent correction magnitudes.

The results refine the understanding of hadronic effects on muon $g-2$.

Abstract

We consider the subleading contributions of the hadronic vacuum polarization, involving the $\pi^0\gamma^*\gamma^*$ transition form factor, to the muon anomalous magnetic moment $g-2$. Various models for the form factor, based on hadronic ansatzes and holographic principles, are considered: They are the Wess-Zumino-Witten, vector meson dominance, lowest meson dominance (one and two vector resonances) models, and AdS/QCD. The model parameters are determined by fitting the experimental data for the $e^+ e^- \rightarrow \pi^0 \gamma$ total cross section. We report numerical results of the corrections to the muon $g-2$ that the resulting values of two vector resonances model are of order-of-magntitude smaller than the one obtained from the dispersion relation.