Lepton masses and mixing angles from heterotic orbifold models

We systematically study the possibility for realizing realistic values of lepton mass ratios and mixing angles by using only renormalizable Yukawa couplings derived from heterotic $Z_6$-I orbifold. We assume one pair of up and down sector Higgs fields. We consider both the Dirac neutrino mass scenario and the seesaw scenario with degenerate right-handed majorana neutrino masses. It is found that realistic values of the charged lepton mass ratios, $m_e/m_\tau$ and $m_\mu/m_\tau$, the neutrino mass squared difference ratio, $\Delta m^2_{31}/\Delta m^2_{21}$, and the lepton mixing angles can be obtained in certain cases.