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 $Y^{a\beta }$ that connect neutrinos and clockwork fermions, nine clockwork mass ratios $q_{a\beta }$, and nine numbers of clockwork fermions $n_{a\beta }$, where $a,\beta =1,2,3$. Assuming $|Y^{a\beta }|=1$, 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 $q_{a\beta }$ origin scenario. In the $n_{a\beta }$ origin scenario, the correct order of magnitude of the observed neutrino mixings is obtained from a clockwork model.

Comments: 9 pages, 4 figures. Accepted for publication in Physical Review D