Muon Anomalous Magnetic Moment and Right-Handed Sterile Neutrino

Abstract The muon’s magnetic moment is a fundamental quantity in particle physics and the observed deviation of its value from the prediction of quantum electrodynamics motivated investigations beyond the Standard Model (SM). In this study, we utilize the effective coupling of right-handed sterile neutrinos with SM gauge bosons to calculate the muon anomalous magnetic moment ($\boldsymbol{\mu }$AMM) at one-loop level. The contribution of the sterile neutrino interactions on the $\boldsymbol{\mu }$AMM is evaluated by including both standard and nonstandard neutrino interactions. Our analysis shows that the standard sterile neutrino interactions give a negligible contribution to $\Delta a_{\boldsymbol{\mu }}$ while the nonstandard neutrino interactions can play a significant role in explaining the $(g-2)_{\boldsymbol{\mu }}$ anomaly. In the context of the nonstandard neutrino interaction, our calculation shows that a Dirac mass scale $M_\mathrm D\approx 100\, \text{GeV}$ could explain the muon anomaly if the right-handed sterile neutrino’s coupling with SM particles is about $\mathcal {G}_R\approx 10^{-3}$. Furthermore, we use the observed discrepancy in the muon anomalous magnetic moment to impose constraints on the model parameters. We present the allowed parameter space, consistent with the experimental data on $\Delta a_{{\boldsymbol{\mu }}}^{\mathrm{ SN}}$, and discuss the percentage of the ${\boldsymbol{\mu }}$ anomaly compensation in terms of the coupling constant $\mathcal {G}_R$.