spectrum [@Ibanez:1982xg; @Barr:2007ma]. The electron mass is estimated to be $$\begin{aligned}
m_{e} \sim \frac{Y^2_{4}}{16\pi^2}\frac{m^2_{H}}{m_{L+R,3}} \approx \frac{Y^2_{4}}{16\pi^2Y_{S2}}\frac{m^2_{H}}{V_{S}} \;\;,\end{aligned}$$ where we ignore both mixings in lepton and scalar sectors and $m_{H}$ represents the common mass scale of scalars for simplicity. By using Eq. (\[chargemass\]) we have the relation $m_{e}/m_{\mu} \approx \frac{Y_{4}m^2_{H}}{16\pi^2Y_{S2}V_{S}V'} \approx \frac{\alpha}{\pi}$. We should point out that the result depends sensitively on several parameters as in many previous works [@Georgi:1972hy; @Barr:1976bk; @Barr:1978rv; @Balakrishna:1988xg; @Ibanez:1982xg]; however, a recent study in Refs. [@Barr:2007ma] indicates that the parameters could be reduced considerably.

![A 1-loop diagram which gives the electron a finite small mass through new vector leptons.[]{data-label="fig:e-mass"}](e-mass.eps){width="30.00000%"}

Note that the charged lepton are given masses by the VEV $\langle H'_{4} \rangle$ which is not directly related to the neutrino masses, so we can calculate the mass eigenstates of charged leptons by using the biunitary transformations to diagonalize the mass matrix $M_{l}$. The rotation matrix of left-handed fields can be absorbed into the redefinition of Higgses $H'_{1}$ and $H'_{3}$, while the rotation of the right-handed charged leptons will not affect the tribimaximal mixings for neutrinos at leading order.

Neutrino Masses
---------------

We next turn to the neutrino masses. The full neutrino mass matrix in the 