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

Abstract

Abstract The MSSM is extended to the $$U(1)_X$$ U ( 1 ) X SSM, whose local gauge group is $$SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_X$$ S U ( 3 ) C × S U ( 2 ) L × U ( 1 ) Y × U ( 1 ) X . To obtain the $$U(1)_X$$ U ( 1 ) X SSM, we add the new superfields to the MSSM, namely: three Higgs singlets $${\hat{\eta }},~\hat{{\bar{\eta }}},~{\hat{S}}$$ η ^ , η ¯ ^ , S ^ and right-handed neutrinos $${\hat{\nu }}_i$$ ν ^ 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 $$U(1)_X$$ 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 $$7.4\times 10^{-10}$$ 7.4 × 10 - 10 , which can remedy the deviation between SM prediction and experimental data to some extent.