Therefore, the Higgs associated LFV processes can become important in a scenario with the soft-SUSY-breaking scale $m_{\rm SUSY}^{}$ to be much higher than the electroweak one. In the MSSM, predicted values of $|\kappa_{3i}^L|^2$ can be as large as of ${\cal O}({10^{-6}})$ when $m_{\rm SUSY}^{}$ is a few TeV[@Rossi; @Osaka]. In the MSSM with right-handed neutrinos, left-handed slepton mixing may be a consequence of running effects of the neutrino Yukawa couplings between the scale of the grand unification and that of the right-handed neutrinos[@MSSMRN]. The parameters $\kappa^{L}_{3i}$ are mainly induced by mixing of left-handed sleptons[@BK; @DER; @Sher-tmeta; @Rossi; @Osaka; @Herrero]. The LFV Yukawa interactions can also appear effectively in the Zee model[@Zee]. The LFV parameters $\kappa^{L,R}_{ij}$ are induced through flavor violating couplings in the charged scalar interactions with leptons.

  Mode                                  Belle (90% CL)                            BaBar (90% CL)
  ------------------------------------- ----------------------------------------- -------------------------------------
  $\tau^-\rightarrow e^-\pi^0$          [@belle-tau-lp0]                          
  $\tau^-\rightarrow e^-\eta$           [@belle-tau-lp0]                          
  $\tau^-\rightarrow e^-\eta'$          [@belle-tau-lp0]                          
  $\tau^-\rightarrow \mu^-\pi^0$        [@belle-tau-lp0]                          
  $\tau^-\rightarrow \mu^-\eta$         [@belle-tau-lp0]                          
  $\tau^-\rightarrow \mu^-\eta'$        [@belle-tau-lp0]                          
  $\tau^-\rightarrow e^-\pi^+\pi^-$     $8.4\times 10^{-7}$[@belle-tau-lMM]       [@babar-tau-lMM]
  $\tau^-\rightarrow e^-\pi^+K^-$       $5.7\times 10^{-7}$[@belle-tau-lMM]       [@babar-tau-lMM]
  $\tau^-\rightarrow e^-K^+\pi^-$       $5.6\times 10^{-7}$[@belle-tau-lMM]       [@babar-tau-lMM]
  $\tau^-\rightarrow e^-K^+K^-$         $3.0\times 10^{-7}$[@belle-tau-lMM]       [@babar-tau-lMM]
  $\tau^-\rightarrow \mu^-\pi^+\pi^-$   [@belle-tau-lMM]                          $2.9\times 10^{-7}$[@babar-tau-lMM]
  $\tau^-\rightarrow \mu^-\pi^+K^-$     $6.3\times 10^{-7}$[@belle-tau-lMM]       [@babar-tau-lMM]
  $\tau^-\rightarrow \mu^-K^+\pi^-$     $15.5\times 10^{-7}$[@belle-tau-lMM]      [@babar-tau-lMM]
  $\tau^-\rightarrow \mu^-K^+K^-$       $11.7\times 10^{-7}$[@belle-tau-lMM]      [@babar-tau-lMM]
  $\tau^-\rightarrow e^-e^+e^-$         $3.5\times10^{-7}$[@belle-tau-3l]         [@babar-tau-3l]
  