Study some two loop contribution to muon anomalous MDM in the N-B-LSSM

Abstract It is well known that the muon magnetic dipole moment (MDM) has close relation with the new physics (NP) in the development of the Standard Model (SM). Combined with the Fermilab National Accelerator Laboratory (FNAL) and the Brookhaven National Laboratory (BNL) E821 result, the departure from the SM prediction is about 5.0 $$\sigma .$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> We study the electroweak corrections from several type two-loop SUSY diagrams and the virtual SUSY particles include chargino, neutralino, scalar lepton and scalar neutrino. Based on the latest experimental constraints, we study the muon anomalous MDM under the next to the minimal supersymmetric extension of the SM with local B-L gauge symmetry (N-B-LSSM). The abundant numerical results verify that $$\tan {\beta },$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>tan</mml:mo> <mml:mi>β</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> $$T_{e22}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mn>22</mml:mn> </mml:mrow> </mml:msub> </mml:math> , $$~M^2_L,~M^2_e,~M_{BB'}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>B</mml:mi> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> play an important role in muon anomalous MDM. $$M^2_e,~\tan {\beta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>e</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mo>tan</mml:mo> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> and $$~T_{e22}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mn>22</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> are sensitive parameters to muon anomalous MDM. From the data obtained in all the figures of the numerical results, most of the values of $$a_{\mu }^{NBL}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>NBL</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> are in 2 $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> interval, which can compensate the departure between the experiment data and the SM prediction.