Twisted Family Structure and Neutrino Large Mixing

Abstract

I demonstrate that neutrino large mixing between ${\nu }_{\mu }$ and ${\nu }_{\tau }$ are naturally reproduced using a novel mechanism called `E-twisting'in a supersymmetric $E_6$ grand unification model. This model explains all the characteristic features of the quark/lepton Dirac masses as well as the neutrino's Majorana masses despite the fact that all the members in {\bf27} of each generation are assigned a common family charge. Most remarkably, this model yields a novel relation which gives the 2-3 lepton mixing angle ${\theta }_{\mu \tau }$ in terms of quark masses and CKM mixing: $\tan {\theta }_{\mu \tau }=(m_b/m_s)V_{cb}$, which is a kind of SO(10) GUT relation similar to the celebrated SU(5) bottom-tau mass ratio. This relation is a result of a common `twisted SO(10)' structure.+

Comments: 4 pages, LaTeX, conference proceeding