Muon anomalous magnetic moment and Right handed sterile neutrino

TL;DR

The muon anomalous magnetic moment exhibits a notable deviation from the SM prediction, motivating beyond-SM explanations. The authors employ an effective model with right-handed sterile neutrinos generated by four-fermion operators, yielding energy-dependent right-handed couplings $\mathcal{G}_R$ to SM gauge bosons and computing the one-loop corrections to $a_{\boldsymbol{\mu}}$ from both standard and non-standard neutrino interactions. They find that standard sterile-neutrino interactions give negligible $\Delta a_{\boldsymbol{\mu}}$, while non-standard W-mediated diagrams with left-right mixing can significantly contribute; in particular, a Dirac mass scale $M_D\sim 100$ GeV and $\mathcal{G}_R\sim 10^{-3}$ can account for the observed discrepancy, with larger $\mathcal{G}_R$ (around $5\times 10^{-3}$) potentially explaining the full anomaly. The work delineates viable parameter space within this effective framework and motivates further exploration of LFV constraints and electron/tau channel implications for sterile-neutrino scenarios addressing $a_{\boldsymbol{\mu}}$.

Abstract

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 ($\boldsymbolμ$AMM) at one-loop level. The contribution of the sterile neutrino interactions on the $\boldsymbolμ$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 $Δa_{\boldsymbolμ}$ 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 $Δa_{\boldsymbolμ}^{SN}$ and discuss the percentage of the ${\boldsymbolμ}$ anomaly compensation in terms of the coupling constant $\mathcal{G}_R$.

Figures (8)

• Figure 1: Lowest-order SM corrections to $a_{\mu}$. From left to right: QED, weak, and hadronic Lindner:2016bgg.
• Figure 2: The possible sunset diagrams from the second term of (\ref{['art1']}), namely, sterile neutrino and SM fermion four-fermion interactions $\bar{\nu}^{fc}_{_R}\psi^{f}_{_R}\bar{\psi}^{f}_{_R} \nu^{fc}_{_R}$, in which $\psi^{f}_{_R}$ represents SM right-handed fermions. Hence, these 1PI vertices lead to effective SM gauge boson couplings to right-handed neutrinos (\ref{['rhc0']}). Left: the effective 1PI interacting vertex (\ref{['rhc0']}) of the gauge boson $W^+$ and right-handed sterile neutrino $\nu^\ell_R$, for more details see Figure 3 of Ref. Xue:2015wha. Right: the effective 1PI interacting vertex (\ref{['rhc0']}) of photon $\gamma$ and right-handed sterile neutrino $\nu^\ell_R$, and similar one for $Z^0$ boson. The slightly thick solid lines inside sunset diagrams represent right-handed neutrino propagators with Dirac mass (left) or Majorana mass (right). A Dirac mass term is present in the internal electron propagator from $e_L$ to $e_R$ in the left sunset diagram. Xue:2020cnw.
• Figure 3: The effective coupling of right-handed current with W , Z bosons and photon, which are not present in the SM. The corresponding expressions are Eqs. (\ref{['rhc01']}) and (\ref{['effem1']}).
• Figure 4: The contributions of sterile neutrinos $\nu_R$, SM (Active) neutrinos $\nu_L$ and W bosons to the one-loop vertex correction of the muon anomalous magnetic moment. The red spots indicate the effective interacting vertices depicted in Fig. \ref{['fig1']}, which are absent in the SM.
• Figure 5: The percentage of the $a_{\boldsymbol{\mu}}$ anomaly compensation in terms of $\mathcal{G}_R$. Note: $\delta a_{{\boldsymbol{\mu}}}$ stands for $\delta a_{{\boldsymbol{\mu}}}=10^9 \Delta a_{{\boldsymbol{\mu}}}$