The order analysis for the two loop corrections to lepton MDM
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Regular Article - Theoretical Physics
The order analysis for the two loop corrections to lepton MDM Shu-Min Zhao1,2,a , Xing-Xing Dong1,2,b , Lu-Hao Su1,2 , Hai-Bin Zhang1,2 1 2
Department of Physics, Hebei University, Baoding 071002, China Key Laboratory of High-precision Computation and Application of Quantum Field Theory of Hebei Province, Baoding 071002, China
Received: 9 April 2020 / Accepted: 26 August 2020 © The Author(s) 2020
Abstract The experimental data of the magnetic dipole moment(MDM) of lepton(e, μ) is very exact. The deviation between the experimental data and the standard model prediction maybe come from new physics contribution. In the supersymmetric models, there are very many two loop diagrams contributing to the lepton MDM. In supersymmetric models, we suppose two mass scales M S H and M with M S H M for supersymmetric particles. Squarks belong to M S H and the other supersymmetric particles belong to M. We analyze the order of the contributions from the two loop diagrams. The two loop triangle diagrams corresponding to the two loop self-energy diagram satisfy Ward-identity, and their contributions possess particular factors. This work can help to distinguish the important two loop diagrams giving corrections to lepton MDM.
1 Introduction With the detection of the 125 GeV Higgs boson [1,2], the standard model (SM) achieves great success. However, SM has some short comings: (1) SM can not give masses to neutrinos; (2) SM does not have cold dark matter candidate. The minimal supersymmetric(SUSY) extension of the standard model(MSSM) [3] has attracted physicists’ attentions for more than 30 years. MSSM has also been extended, and the extensions of MSSM [4–6] have many particles beyond SM. These new particles give corrections to the studied processes. For the magnetic dipole moment (MDM) [7–9] of lepton especially muon, the two loop corrections from SUSY particles are important. In the SM, there are several parts giving the contributions to lepton MDM [10,11] QE D
alS M = al
+ alE W + alH AD .
(1)
a e-mail:
[email protected] (corresponding author)
b e-mail:
[email protected]
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QE D
al representing the QED contribution is dominant. While, alE W and alH AD denote the electroweak and hadronic contributions, respectively. For muon MDM, the deviation between the SM theoretical prediction and experimental data is about 3.7σ [12,13] aμ = aμex p − aμS M = (27.4 ± 7.3) × 10−10 .
(2)
This deviation aμ may come from the new physics contribution. In SUSY models, there are many SUSY particles that correct muon MDM through loop diagrams. As discussed in the works [14–17], the two loop SUSY diagrams can contribute importantly to muon MDM. With the on-shell renormalization scheme, the numerical calculation of two loop electroweak corrections to the muon MDM has been performed in the SM [18]. Physicists show great interests on new physics corrections to muon MDM. The authors of Ref. [19] study the 2HDM contribution to the muon MDM and present the complete two loop results. It
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