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At current and future LFV experiments, the coupling constants f$_{ij}$ and g$_{ij}$ can be further tested via the LFV rare decays such as ℓ → ℓ $^{′}$γ and ℓ → ℓ $^{′}$ℓ$^{′}$ℓ$^{′′}$. The same operators as in ℓ − → ℓ $^{′∓}$e$^{−}$e± would also be tested directly at the ILC via e $^{±}$e− → ℓ $^{−}$ℓ $^{$^{′}$±}$. In the scenario in Eq. (11), we estimate that σ ( e $^{+}$e − → µ $^{±}$τ $^{∓}$) ∼ 5 fb for √$_{s}$ = 1 TeV. When we take g$_{ee}$ = 0 . 4, g$_{eτ}$ = 0 . 01, m$_{k}$ = µ = 1 . 2 TeV and m$_{ω}$ = 400 GeV, which also satisfy all the current data, we obtain σ ( e $^{+}$e − → τ $^{±}$e$^{∓}$) ∼ 0 . 76 (1.7) fb for √$_{s}$ = 500 GeV (1 TeV). 

## The Ma model 

In the Ma model, the coupling constants ˆ h α e ( α = 1 , 2) 7 are strongly constrained from neutrino data and LFV data. As a typical choice of parameters, we consider 8 

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in which the normal neutrino mass hierarchy is realized. Because ˆ h α e are very small for a 

