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Register a new userStudy muon g-2 at two loop level in the $U(1)_X$SSM
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The new experiment data of muon g-2 is consistent with the previous data of Fermion lab, and the departure from SM prediction is about 4.2 $sigma$. It strengthens our faith in the new physics. $U(1)_X$SSM is the U(1) extension of the minimal supersymmetric standard model, where we study the electroweak corrections to the anomalous magnetic dipole moment of muon from the one loop diagrams and some two loop diagrams possessing important contributions. These two loop diagrams include Barr-Zee type, rainbow type and diamond type. The virtual supersymmetric particles in these two loop diagrams are chargino, scalar neutrino, neutralino, scalar lepton, which are supposed not very heavy to make relatively large corrections. We obtain the Wilson coefficients of the dimension 6 operators inducing the anomalous magnetic dipole moment of muon. The numerical results can reach $25times 10^{-10}$ and even larger.
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The MSSM is extended to the $U(1)_X$SSM, whose local gauge group is $SU(3)_C times SU(2)_L times U(1)_Y times U(1)_X$. To obtain the $U(1)_X$SSM, we add the new superfields to the MSSM, namely: three Higgs singlets $hat{eta},~hat{bar{eta}},~hat{S}$ and right-handed neutrinos $hat{ u}_i$. 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 $U(1)_X$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 $7.4times10^{-10}$, which can remedy the deviation between SM prediction and experimental data to some extent.
In the $U(1)_X$ extension of the minimal supersymmetric standard model, we study a two step phase transition for the universe. The first step happens at high temperature from origin to z coordinate axis. The second step is the electroweak phase transition(EWPT) with barrier between two minima, which is the first order EWPT. We study the condition for this type phase transition to occur. The strong first order EWPT is our expection, and with the supposed parameters the evolution of the universe is plotted by the figures.
Two-loop electroweak corrections to the muon anomalous magnetic moment are automatically calculated by using GRACE-FORM system, as a trial to extend our system for two-loop calculation. We adopt the non-linear gauge (NLG) to check the reliability of our calculation. In total 1780 two-loop diagrams consisting of 14 different topological types and 70 one-loop diagrams composed of counter terms are calculated. We check UV- and IR-divergences cancellation and the independence of the results from NLG parameters. As for the numerical calculation, we adopt trapezoidal rule with Double Exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR- divergence and to get finite values.
We present an economical model where an $S^{}_1$ leptoquark and an anomaly-free $U(1)^{}_X$ gauge symmetry with $X = B^{}_3-2L^{}_mu/3-L^{}_tau/3$ are introduced, to account for the muon anomalous magnetic moment $a^{}_mu equiv (g^{}_mu-2)$ and flavor puzzles including $R^{}_{K^{(ast)_{}}}$ and $R^{}_{D^{(ast)_{}}}$ anomalies together with quark and lepton flavor mixing. The $Z^prime_{}$ gauge boson associated with the $U(1)^{}_X$ symmetry is responsible for the $R^{}_{K^{(ast)_{}}}$ anomaly. Meanwhile, the specific flavor mixing patterns of quarks and leptons can be generated after the spontaneous breakdown of the $U(1)^{}_X$ gauge symmetry via the Froggatt-Nielsen mechanism. The $S^{}_1$ leptoquark which is also charged under the $U(1)^{}_X$ gauge symmetry can simultaneously explain the latest muon $(g-2)$ result and the $R^{}_{D^{(ast)_{}}}$ anomaly. In addition, we also discuss several other experimental constraints on our model.
Numerical calculation of two-loop electroweak corrections to the muon anomalous magnetic moment ($g$-2) is done based on, on shell renormalization scheme (OS) and free quark model (FQM). The GRACE-FORM system is used to generate Feynman diagrams and corresponding amplitudes. Total 1780 two-loop diagrams and 70 one-loop diagrams composed of counter terms are calculated to get the renormalized quantity. As for the numerical calculation, we adopt trapezoidal rule with Double Exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR-divergences and to get finite values. The reliability of our result is guaranteed by several conditions. The sum of one and two loop electroweak corrections in this renormalization scheme becomes $a_mu^{EW:OS}[1{rm+}2{rm -loop}]= 151.2 (pm 1.0)times 10^{-11}$, where the error is due to the numerical integration and the uncertainty of input mass parameters and of the hadronic corrections to electroweak loops. By taking the hadronic corrections into account, we get $a_mu^{EW}[1{rm+}2 {rm -loop}]= 152.9 (pm 1.0)times 10^{-11}$. It is in agreement with the previous works given in PDG within errors.
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