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Lepton flavor violating decays $τ\rightarrow{Pl}$ in the $U(1)_X$SSM model

$U(1)_X$SSM is the extension of the minimal supersymmetric standard model(MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to MSSM. In the framework of $U(1)_X$SSM, we study lepton flavor violating decays $τ\rightarrow{Pl}(P=π,~η,~η^\prime;~l=μ,~e)$. According to the latest experimental data of $τ\rightarrow{Pe}$ and $τ\rightarrow{Pμ}$, the influence of different sensitive parameters on the results is analyzed to make a reasonable prediction for future experiments. From the numerical analysis, the non-diagonal elements which correspond to the generations of the initial lepton and final lepton are main sensitive parameters and lepton flavor violation(LFV) sources. This work can provide a basis for finding the existence of new physics(NP).