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 $\mu \rightarrow 3e$ and $\tau\rightarrow3\mu$ 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 $\ell_{i}\rightarrow\ell_{j}\nu_{\ell}\nu_{\ell}$, $\tau\rightarrow\mu P $ and $P\rightarrow \mu e$ with $P=\pi^{0},\eta$ and $\eta '$. 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 $Br(\tau\rightarrow\mu\nu_{\ell}\nu_{\ell})$ reach $1.1\times10^{-7}$. All $Z'$ models considered in this paper can produce significant contributions to the process $\tau\rightarrow\mu P$. However, the value of $Br(P\rightarrow\mu e)$ is far below its corresponding experimental upper bound. 
Chong-Xing Yue and Man-Lin Cui
hep-ph