Heavy neutrino threshold effects in low energy phenomenology

Right handed neutrinos with mass of $\mathcal{O}({10}^{12}-{10}^{13})$ GeV are required to implement the see-saw mechanism and generate neutrino masses capable of playing a role in structure formation. Moreover models of fermion masses often relate the Yukawa couplings involving these neutrinos to the up-quark Yukawa couplings. Here we study the effects of such couplings on the radiative corrections to quark masses. We find that $b-\tau$ equality at $M_{GUT}$ may still give the correct $m_b\mathrm{/}{m}_{\tau }$– ratio at low energies, but only if there is large $\mu -\tau$ mixing in the charged leptonic sector. We propose specific mass matrix ``textures’’ dictated by a $U(1)$ family symmetry whose structure preserves $m_b=m_{\tau }$ at $M_{GUT}$. In these schemes, due to the large ${\nu }_{\mu }-{\nu }_{\tau }$ mixing, it is possible to give a simultaneous solution to the solar neutrino deficit and the atmospheric neutrino problem.