Maximal atmospheric neutrino mixing in an SU(5) model

Abstract

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the $U(1)_F$ symmetry associated with a suitably defined family number $F$, together with a $\mathbbm{Z}_2$ symmetry which does not commute with $F$. $U(1)_F$ is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in addition, $U(1)_F$ is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale $10^{16} \mathrm{GeV} < m_U < 10^{19} \mathrm{GeV}$; indeed, we have found a particular solution to this problem which yields results almost identical to the ones of the Minimal Supersymmetric Standard Model.