Lepton flavor violation in $\ensuremath{\tau}$ and $\ensuremath{\mu}$ processes is studied in the littlest Higgs model with $T$ parity. We consider various asymmetries defined in polarized $\ensuremath{\tau}$ and $\ensuremath{\mu}$ decays. Correlations among branching ratios and asymmetries are shown in the following lepton flavor violation processes: ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\gamma}$, ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}{e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{\ensuremath{-}}A\ensuremath{\rightarrow}{e}^{\ensuremath{-}}A$ ($A=\mathrm{Al}$, Ti, Au, and Pb), ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\gamma}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}P$ ($P={\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$), ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}V$ ($V={\ensuremath{\rho}}^{0}$, $\ensuremath{\omega}$ and $\ensuremath{\phi}$), ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\gamma}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}{e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}P$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}V$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$ and ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}{e}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. It is shown that large parity asymmetries and time-reversal asymmetries are allowed in ${\ensuremath{\mu}}^{+}\ensuremath{\rightarrow}{e}^{+}{e}^{+}{e}^{\ensuremath{-}}$. For $\ensuremath{\tau}$ lepton flavor violation processes, sizable asymmetries are possible reflecting characteristic chirality structure of lepton flavor violating interactions in this model.
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