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

We examine contributions to the muon dipole moment $g-2$ from a 3-form field $\mathrm{\Omega }$, 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 $\mathrm{\Omega }$-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 $\mathrm{\Omega }$, we have still found a substantial parameter space which can accommodates the muon $g-2$ data.