Exclusions on $Z'$ mass and its non-universal couplings in LFV decays

This letter presents a phenomenological analysis for the lepton ($l_i^{}$) decaying into $l_j^{} l_k^{} \bar{l}_k^{}, l_j^{} \pi^+ \pi^-$ considering family non-universal couplings as source of the lepton flavor-violating (LFV) currents and a new neutral gauge boson ($Z'$) as mediator in the flavor-changing. The most viable $g_{V}^{f_if_J}$ and $g_{A}^{f_if_j}$ couplings are reported as long as derive new bounds for the $M_{Z'}^{}$ by using current results from LHC and a phenomenological analysis.