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

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.

Study of lepton EDMs in the U(1) X SSM *

“…This effect can also be induced by RGEs, even with a zero value at . The general form of the covariant derivative of this model is [33][34][35]…”

Study muon g-2 at two-loop level in the $U(1)_X$SSM

“…One can find the concrete forms of H L,R H F1 F 2 and H L,R W F1 F 2 in the Ref. [30]. Using similar assumption m F = m F 1 = m F 2 ≫ m h 0 , one can simplify the two loop Barr-Zee type diagrams contributing to the lepton MDMs for the Figs.…”

“…In the U(1) X SSM, we have researched several processes [29,30]. In this section, the numerical results are studied and the used parameters can satisfy the the experimental constraints.…”

“…In our previous work, we calculate the contributions from some two loop diagrams to muon MDM under the U(1) X SSM with the effective Lagrangian method. In this work, we research one loop diagrams and more two loop diagrams than our previous work [30]. To make up the departure between experiment data and SM prediction for a µ , the scalar neutrino and scalar lepton should not be heavy.…”

“…The neutral CP-even Higgs mass squared matrix is 5 × 5, because of the introduction of η, η and S. The lightest CP even Higgs mass can be improved at tree level. The particle contents can be found in our previous work [29,30].…”