The two-loop contributions to muon MDM in $U(1)_X$ SSM

TL;DR

This paper calculates two-loop contributions to the muon magnetic dipole moment in the $U(1)_X$ extended supersymmetric model, exploring potential new physics effects that could explain deviations from the Standard Model.

Contribution

It provides the first detailed analysis of two-loop diagrams, including Barr-Zee and rainbow types, in the $U(1)_X$SSM for muon MDM calculations.

Findings

Numerical results reach $7.4\times10^{-10}$, addressing the muon g-2 anomaly.

Two-loop contributions can partially explain the deviation from the Standard Model.

Inclusion of Z-Z rainbow diagrams enhances the accuracy of the muon MDM prediction.

Abstract

The MSSM is extended to the $U(1)_X$SSM, whose local gauge group is $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_X$. To obtain the $U(1)_X$SSM, we add the new superfields to the MSSM, namely: three Higgs singlets $\hat{\eta},~\hat{\bar{\eta}},~\hat{S}$ and right-handed neutrinos $\hat{\nu}_i$. It can give light neutrino tiny mass at the tree level through the seesaw mechanism. The study of the contribution of the two-loop diagrams to the MDM of muon under $U(1)_X$SSM provides the possibility for us to search for new physics. In the analytical calculation of the loop diagrams (one-loop and two-loop diagrams), the effective Lagrangian method is used to derive muon MDM. Here, the considered two-loop diagrams include Barr-Zee type diagrams and rainbow type two-loop diagrams, especially Z-Z rainbow two-loop diagram is taken into account. The obtained numerical results can reach $7.4\times10^{-10}$, which can remedy the deviation between SM prediction and experimental data to some extent.