The anomalous magnetic moment of the electron is determined experimentally with an accuracy of $2.8\times 10^{-13}$ and the uncertainty may decrease by an order of magnitude in the future. While the current data are in excellent agreement with the standard model, the possible future improvement in the error in $\mathrm{\Delta }{a}_e=a_e^{\exp }-a_e^{\text{theory}}$ has recently drawn interest in the electron anomalous magnetic moment as a possible probe of new physics beyond the standard model. In this work we give an analysis of such physics in an extension of the minimal supersymmetric standard model with a vector multiplet. In the extended model the electroweak contribution to the anomalous magnetic moment of the electron includes loop diagrams involving in addition to the exchange of W and Z, the exchange of charginos, sneutrinos and mirror sneutrinos, and the exchange of neutralinos, sleptons and mirror sleptons. The analysis shows that a contribution to the electron magnetic moment much larger than expected by $m_e^2/m_{\mu }^2$ scaling of the deviation of the muon anomalous magnetic moment over the standard model prediction, i.e., $\mathrm{\Delta }{a}_{\mu }=3\times 10^{-9}$ as given by the Brookhaven experiment, can be gotten within the minimal supersymmetric standard model (MSSM) extension. Effects of $CP$ violating phases in the extended MSSM model on the corrections to the supersymmetric electroweak contributions to $a_e$ are also investigated. The analysis points to the possibility of detection of new physics effects with modest improvement on the error in $\mathrm{\Delta }{a}_e=a_e^{\exp }-a_e^{\text{theory}}$.

• Received 25 March 2014

DOI:https://doi.org/10.1103/PhysRevD.89.093016