Muon anomalous magnetic moment and Right handed sterile neutrino

The muon's magnetic moment is a fundamental quantity in particle physics and the deviation of its value from quantum electrodynamics (QED), motivates research beyond the standard models (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 calculated by considering the standard and non-standard neutrino interactions. Our results show that the standard sterile neutrino interactions give a negligible contribution to $\Delta a_{\boldsymbol{\mu}}$ while the non-standard neutrino interactions can play a significant role in explaining the muon $(g-2)$ anomaly. In the context of the non-standard neutrino interaction, our calculation shows that a Dirac mass scale $M_D$ around $100\,\text{GeV}$ could explain the muon anomaly if the right handed sterile neutrino's coupling with SM particles is about $\mathcal{G}_R\approx 10^{-3}$. We have also plotted the allowed region of the model parameters that satisfy the experimental data on $\Delta a_{{\boldsymbol{\mu}}}^{SN}$ and discuss the percentage of the ${\boldsymbol{\mu}}$ anomaly compensation in terms of the coupling constant $\mathcal{G}_R$.