Clockwork origin of neutrino mixings

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.

Figure 1

The magnitude of the clockwork mass ratio $q_{a\beta }$ for the best-fit values of the squared mass differences and the mixing angles under the normal mass ordering condition, where $n$ denotes the universal number of fermions for all clockwork generations ($n=30$ in the upper panel and $n=50$ in the lower panel).

Figure 2

The magnitude of the effective number of clockwork fermions $n_{a\beta }$ for the best-fit values of the squared mass differences and the mixing angles under the normal mass ordering condition, where $q$ denotes universal clockwork mass ratio ($q=2.0$ in the upper panel and $q=2.5$ in the lower panel).