Clockwork origin of neutrino mixings

Abstract

The clockwork mechanism provides a natural way to obtain hierarchical masses and couplings in a theory. We propose a clockwork model that has nine clockwork generations. In this model, the candidates of the origin of the neutrino mixings are nine Yukawa mass matrix elements $Y^{aβ}$ that connect neutrinos and clockwork fermions, nine clockwork mass ratios $q_{aβ}$, and nine numbers of clockwork fermions $n_{aβ}$, where $a, β=1,2,3$. Assuming $|Y^{aβ}|=1$, the neutrino mixings originate from the pure clockwork sector. We show that the observed neutrino mixings are exactly obtained from a clockwork model in the case of the $q_{aβ}$ origin scenario. In the $n_{aβ}$ origin scenario, the correct order of magnitude of the observed neutrino mixings is obtained from a clockwork model.