Lepton flavor violating tau decays in type-III seesaw mechanism

In this paper, the lepton flavor violating $\tau\to \ell P(V)$ ($P,V= \pi^0, \eta, \eta^{\prime}, \rho^0, \omega, \phi$) and $\tau\to 3\ell$ ($\ell = e, \mu$) decays are studied in the framework of the type-III seesaw model, in which new triplet fermions with a zero hypercharge (Y=0) interact with ordinary lepton doublets via Yukawa couplings, and affect tree-level leptonic Z-boson couplings. We investigate the experimental bound from the leptonic Z decay to get contraint on the exsiting parameters space. We predict that the upper limits on the branching ratios of $\tau\to \ell P(V)$ and $\tau\to 3\ell$ can reach the experimental current limits.