The two-loop contributions to muon MDM in SSM

Lu-Hao Su; Shu-Min Zhao; Xing-Xing Dong; Dan-Dan Cui; Tai-Fu Feng; Hai-Bin Zhang

doi:10.1140/epjc/s10052-021-09219-0

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 433
https://doi.org/10.1140/epjc/s10052-021-09219-0

Regular Article - Theoretical Physics

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

Lu-Hao Su¹^,2^a, Shu-Min Zhao¹^,2, Xing-Xing Dong¹^,2, Dan-Dan Cui¹^,2, Tai-Fu Feng¹^,2^,3 and Hai-Bin Zhang¹^,2

¹ Department of Physics, Hebei University, 071002, Baoding, China
² Key Laboratory of High-Precision Computation and Application of Quantum Field Theory of Hebei Province, 071002, Baoding, China
³ Department of Physics, Chongqing University, 401331, Chongqing, China

^a suluhao0606@163.com

Received: 21 January 2021
Accepted: 10 May 2021
Published online: 20 May 2021

Abstract

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

© The Author(s) 2021

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