Exclusions on $Z^{\mathrm{\prime }}$ 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 ($Z^{\mathrm{\prime }}$) as mediator in the flavor-changing. The most viable $g_V^{f_i{f}_J}$ and $g_A^{f_i{f}_j}$ couplings are reported as long as derive new bounds for the $M_{Z^{\mathrm{\prime }}}^{}$ by using current results from LHC and a phenomenological analysis.