Natural neutrino mass hierarchy in a theory of gauge flavour deconstruction

TL;DR

This work shows that a natural neutrino mass hierarchy with large lepton mixing can emerge in a flavour-deconstructed theory by extending the minimal tri-hypercharge framework to include right-handed neutrinos charged under $U(1)_{R}$ and $U(1)_{(B-L)/2}$. The UV completion decomposes family hypercharges into distinct $B-L$-like groups, introducing two hierarchical right-handed neutrinos that drive sequential dominance, while lepton mixing involves contributions from both the neutrino and charged-lepton sectors. The model yields analytic SD relations for the neutrino and charged-lepton masses and mixing angles, predicts $m_{3}^2 \gg m_{2}^2 \gg m_{1}^2$ with $m_{1}\approx 0$, and naturally incorporates the observed quark mass hierarchies and small CKM mixing. Overall, it provides a dynamical mechanism for lepton flavour structure within flavour deconstruction and suggests high-scale signatures and UV-embedding prospects, such as a possible $SO(10)^3$ unification. The approach offers potential predictivity for the neutrino sector through simple ratios of Yukawa couplings, contrasting with neutrino anarchy.

Abstract

We show how a natural neutrino mass hierarchy with large lepton mixing angles may be achieved in a theory of gauge flavour deconstruction. Hitherto it has been shown that neutrino anarchy may result from such theories, but here we show that this need not necessarily be the case. In particular we consider the minimal tri-hypercharge theory, and show that the decomposition of the family hypercharges into the corresponding $B-L$ gauge groups, together with the charged lepton mass hierarchy, implies the sequential dominance conditions for a neutrino mass hierarchy, where lepton mixing originates from both the neutrino and charged lepton sectors. We present novel and model-independent sequential dominance results applicable to this case, but also useful more generally. We also show how natural quark mass and mixing are included in such a framework.