Contributions to the Muon $g-2$ from a Three-Form Field

TL;DR

This paper investigates how a three-form field, common in fundamental theories, contributes to the muon g-2 anomaly, calculating the effect, analyzing theoretical constraints, and identifying viable parameter space consistent with experimental data.

Contribution

It provides the first calculation of the one-loop contribution of a three-form field to muon g-2 and explores the parameter space under unitarity and perturbativity constraints.

Findings

The three-form field contribution to muon g-2 is finite and calculable.

Despite strong unitarity bounds, there exists a parameter space fitting the muon g-2 data.

The model remains consistent with theoretical constraints within certain parameter ranges.

Abstract

We examine contributions to the muon dipole moment $g-2$ from a 3-form field $\Omega$, which naturally arises from many fundamental theories, such as the string theory and the hyperunified field theory. In particular, by calculating the one-loop Feynman diagram, we have obtained the leading-order $\Omega$-induced contribution to the muon $g-2$, which is found to be finite. Then we investigate the theoretical constraints from perturbativity and unitarity. Especially, the unitarity bounds are yielded by computing the tree-level $\mu^+\mu^-$ scattering amplitudes of various initial and final helicity configurations. As a result, despite the strong unitarity bounds imposed on this model of $\Omega$, we have still found a substantial parameter space which can accommodates the muon $g-2$ data.