Generalized Scaling in Flavor Neutrino Masses

TL;DR

This paper explores a generalized scaling approach to flavor neutrino masses, linking mixing angles and mass ratios, and introduces symmetry-breaking terms to align with experimental data, including non-zero reactor angles.

Contribution

It proposes a generalized scaling ansatz for neutrino masses, derives relations between CP phases and mass phases, and analyzes the impact of symmetry breaking on mixing angles.

Findings

Scaling angles are constrained by mass hierarchy.

Predicted effective Majorana mass |M_ee| ranges for hierarchies.

Relations between CP phases and flavor mass phases are established.

Abstract

Scaling in flavor neutrino masses $M_{ij}$ ($i,j$=$e,\mu,\tau$) can be described by two angles: $\theta_{SC}$ and the atmospheric neutrino mixing angle $\theta_{23}$. For $A$=${\cos ^2}{\theta_{SC}}+{\sin ^2}{\theta_{SC}}t_{23}^4$ and B=${\cos ^2}{\theta_{SC}}-{\sin ^2}{\theta_{SC}}t_{23}^2$, where $t_{23}=\tan\theta_{23}$, our scaling ansatz dictates that $M_{i\tau}/M_{i\mu}$ = $- \kappa_it_{23}$ ($i$=$e,\mu,\tau$) with $\kappa_e$=1, $\kappa_\mu$=B/A and $\kappa_\tau$=1/B and leads to the vanishing reactor neutrino mixing angle $\theta_{13}=0$. This generalized scaling is naturally realized in seesaw textures. To obtain $\theta_{13}\neq 0$ as required by the recent experimental results, we introduce breaking terms of scaling ansatz, which are taken to keep $M_{\mu\tau}/M_{\mu\mu}$ = $- \kappa_\mu t_{23}$ intact even at $\theta_{13}\neq 0$. We derive relations that connect CP violating phases with phases of flavor neutrino masses, which are found to be numerically supported. The angle $\theta_{SC}$ is observed to be $0.91 \lesssim\sin^2\theta_{SC}\lesssim 0.93$ for the normal mass hierarchy and $\sin^2\theta_{SC}\lesssim 0.33$ for the inverted mass hierarchy. Also observed is the size of $|M_{ee}|$ to be measured in neutrinoless double beta decay, which is 0.001-0.004 eV (0.02 eV-0.05 eV) in the normal (inverted) mass hierarchy.