Lepton Flavor Physics in the flipped 3-3-1-1 Model: Non-Universality and Violation

We investigate the flavor violation (FV) of Z decays to leptons at tree level and flavor conserving Z decays to leptons in the frame work of the flipped $SU(3)_C\otimes SU(3)_L \otimes U(1)_X\otimes U(1)_N$,(F3311) model. In addition, we analyze the processes $l_i\rightarrow l_j \gamma$ and the leptonic three-body decay. Using the experimental bounds on these decays we set the constraint on $\sin \phi$ which represents the mixing between Z-Z' boson. The most stringent limits arises from $\mu \rightarrow e \gamma$ decay where $\sin \phi \sim \mathcal{ O}(10^{-3})$. The leptonic three-body decay set lower bound on the mass of the new neural gauge boson $m_{Z'} \geq 3.2TeV$. Using the LUX-ZEPLIN (LZ) experiment data we set bounds to the mass of the dark matter candidates. Subsequently, we investigate the lepton non-universality in B decays within the $F3311$ model by calculating the generic one-loop contribution to the process $u_i\rightarrow d_j e_b \bar{\nu}_a$ in the unitary gauge as well as numerical evaluating the branching ratio $R_D, R_{D^{(*)}},R(X_c)$. We demonstrate that the $F3311$ model can address the $3.3 \sigma$ discrepancies between Standard Model and experimental data. To reaffirm our results, we also analyze the $d \to u$ transitions and $s\to u$ transitions. These two transitions also give consistent result with experiment data. Combine all experiment dat a we obtain the operating region for the mass of the model specifically $m_E \in [6.5, 9 ]TeV$, $m_Q \in [6,11]TeV$ and the dark matter candidate $m_\xi \in [1.5,2 ]TeV$.