$\tau^-\rightarrow e^-\mu^+\mu^-$     [@belle-tau-3l]                           $3.3\times 10^{-7}$[@babar-tau-3l]
  $\tau^-\rightarrow \mu^-e^+e^-$       [@belle-tau-3l]                           $2.7\times 10^{-7}$[@babar-tau-3l]
  $\tau^-\rightarrow \mu^-\mu^+\mu^-$   $2.0\times 10^{-7}$[@belle-tau-3l]        [@babar-tau-3l]
  $\tau\rightarrow e\gamma$             [@belle-tau-egamma]                       
  $\tau\rightarrow \mu\gamma$           $3.1\times 10^{-7}$[@belle-tau-mugamma]   [@babar-tau-mugamma]

  : Current experimental limits on branching ratios of the LFV rare tau decays.[]{data-label="Tab:tau-bound"}

Bound on LFV Yukawa couplings from rare tau decays {#Sec:LFV-tau-decay}
==================================================

In order to constrain the LFV parameters $|\kappa_{3i}^{L}|$ and $|\kappa_{i3}^{R}|$, we take into account the data for rare tau decay processes such as $\tau \rightarrow \ell_i P^0 $, $\tau \rightarrow \ell_i M^+M'^-$, $\tau \rightarrow \ell_i\ell'^+\ell'^-$, and $\tau \rightarrow \ell_i\gamma$, where $P^0$ represents $\pi^0$, $\eta$ and $\eta'$ mesons, $M^\pm$ ($M'^\pm$) does $\pi^\pm$ and $K^\pm$ mesons, and $\ell'^\pm=e^\pm$ and $\mu^\pm$. The list of the current data from the B factories are summarized in Table \[Tab:tau-bound\] [@belle-tau-lp0; @belle-tau-lMM; @babar-tau-lMM; @belle-tau-3l; @babar-tau-3l; @belle-tau-egamma; @belle-tau-mugamma; @babar-tau-mugamma]. These bounds may be improved at the super B factory around a digit[@super-B]. In our analysis, we take the underlined data in Table \[Tab:tau-bound\] as our numerical inputs. The branching ratios for these rare $\tau$ LFV decays are summarized in Ref. [@kot].

Since branching ratios for $\tau^-\to\ell_i^-P^0$, $\tau^-\to\ell_i^-M^+M^-$, $\tau^-\to\ell_i^-\ell'^+\ell'^-$ and $\tau^-\to\ell_i^-\gamma$ depend on different combinations of the Higgs boson masses, independent information can be obtained for the model parameters by measuring each 