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$U(1)_X$SSM is the extension of the minimal supersymmetric standard model(MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \timesU(1)_X$. We study lepton flavor violating (LFV) decays$Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($Z\rightarrow e{\mu}$, $Z\rightarrowe{\tau}$, and $Z\rightarrow {\mu}{\tau}$) and$h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($h\rightarrow e{\mu}$, $h\rightarrowe{\tau}$, and $h\rightarrow {\mu}{\tau}$), in this model. In the numericalresults, the branching ratios of $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ arefrom $10^{-9}$ to $10^{-13}$ and the branching ratios of$h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-3}$ to $10^{-9}$, whichcan approach the present experimental upper bounds. Based on the latestexperimental data, we analyze the influence of different sensitive parameterson the branching ratio, and make reasonable predictions for future experiments.The main sensitive parameters and LFV sources are the non-diagonal elementscorresponding to the initial and final generations of leptons, which can beseen from the numerical analysis.

physical review. d/physical review. d.

$Z$ boson decays $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ and Higgs boson  decays $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ with lepton flavor violation in  a $U(1)$ extension of the MSSM