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Considering the constraints on the lepton flavor violating (LFV) couplings of the new gauge boson $Z'$ to ordinary leptons from the experimental upper limit for the LFV process $\ell\rightarrow 3\ell'$, we calculate the contributions of $Z'$ to the LFV decays $V\rightarrow\ell_{i}\ell_{j}$ with $V\in\{\phi,J/\Psi,\Psi(2S),\Upsilon^{(n)}\}$ and $\tau\to\mu(e)\phi$ in the context of several $Z'$ models.
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