Study lepton flavor violation $B^0\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ within the Mass Insertion Approximation

Abstract: We study lepton flavor violating (LFV) decays $B^0\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ ($B^0\rightarrow e{\mu}$, $B^0\rightarrow e{\tau}$ and $B^0\rightarrow {\mu}{\tau}$) in the $U(1)_X$SSM (SSM is acronym for the supersymmetric standard model), which is the $U(1)_X$ extension of the minimal supersymmetric standard model (MSSM). The local gauge group of $U(1)_X$SSM is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. These processes ($B^0\rightarrow e{\mu}$, $B^0\rightarrow e{\tau}$ and $B^0\rightarrow {\mu}{\tau}$) are strictly forbidden in the standard model (SM), but these LFV decays are a signal of new physics (NP). We use the Mass Insertion Approximation (MIA) to find sensitive parameters that directly influence the result of the branching ratio of LFV decay $B_d\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$. Combined with the latest experimental results, we analyze the relationship between different sensitive parameters and the branching ratios of the three processes. According to the numerical analysis, these elements are very restricted from the non observation of CLFV.