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LFV couplings of the extra gauge boson Z' and leptonic decay and production of pseudoscalar mesons

Considering the constraints of the lepton flavor violating (LFV) processes $μ\rightarrow 3e$ and $τ\rightarrow3μ$ on the LFV couplings $Z'\ell_{i}\ell_{j}$, in the contexts of the $E_{6}$ models, the left-right (LR) models, the "alternative" left-right (ALR) models and the 331 models, we investigate the contributions of the extra gauge boson $Z'$ to the decay rates of the processes $\ell_{i}\rightarrow\ell_{j}ν_{\ell}ν_{\ell}$, $τ\rightarrowμP $ and $P\rightarrow μe$ with $P=π^{0},η$ and $η'$. Our numerical results show that the maximal values of the branching ratios for these processes are not dependent on the $Z'$ mass $M_{Z'}$ at leader order. The extra gauge boson $Z'_{X}$ predicted by the $E_{6}$ models can make the maximum value of the branching ratio $Br(τ\rightarrowμν_{\ell}ν_{\ell})$ reach $1.1\times10^{-7}$. All $Z'$ models considered in this paper can produce significant contributions to the process $τ\rightarrowμP$. However, the value of $Br(P\rightarrowμe)$ is far below its corresponding experimental upper bound.