Rare decays of theτlepton as a probe of the left-right-symmetric theories of weak interactions

We consider the flavor-changing rare decays of the $\tau$ lepton as a probe on the left-right-symmetric theories of weak interactions manifesting at the TeV energy scale. We find the branching ratios for the rare decays such as $\tau \to 3\mu$ and $\tau \to \mu \mathrm{ee}$, etc., as large as ${10}^{-5\mathrm{}}$ and those for the radiative decays such as $\tau \to \mu \gamma$ and $\tau \to e\gamma$ as large as 4 × ${10}^{-6\mathrm{}}$, consistent with the existing bounds on the model if the neutrino is a Majorana fermion with its small mass accounted for by the seesaw mechanism. On the other hand, for the case of Dirac neutrinos with a small $m_{\nu }$ accounted for by the loop mechanism, these rare decay modes are suppressed to the level of ${10}^{-10\mathrm{}}$ or less.