Testing constrained sequential dominance models of neutrinos

Constrained sequential dominance (CSD) is a natural framework for implementing the see-saw mechanism of neutrino masses which allows the mixing angles and phases to be accurately predicted in terms of relatively few input parameters. We analyze a class of CSD($n$) models where, in the flavour basis, two right-handed neutrinos are dominantly responsible for the "atmospheric" and "solar" neutrino masses with Yukawa couplings to $(\nu_e, \nu_{\mu}, \nu_{\tau})$ proportional to $(0,1,1)$ and $(1,n,n-2)$, respectively, where $n$ is a positive integer. These coupling patterns may arise in indirect family symmetry models based on $A_4$. With two right-handed neutrinos, using a $\chi^2$ test, we find a good agreement with data for CSD(3) and CSD(4) where the entire PMNS mixing matrix is controlled by a single phase $\eta$, which takes simple values, leading to accurate predictions for mixing angles and the magnitude of the oscillation phase $|\delta_{CP}|$. We carefully study the perturbing effect of a third "decoupled" right-handed neutrino, leading to a bound on the lightest physical neutrino mass $m_1 \lesssim 1$ meV for the viable cases, corresponding to a normal neutrino mass hierarchy. We also discuss a direct link between the oscillation phase $\delta_{CP}$ and leptogenesis in CSD($n$) due to the same see-saw phase $\eta$ appearing in both the neutrino mass matrix and leptogenesis.