Common origin ofμ−τandCPbreaking in the neutrino seesaw, baryon asymmetry, and hidden flavor symmetry

Abstract

We conjecture that all $CP$ violations (both Dirac and Majorana types) arise from a common origin in the neutrino seesaw. With this conceptually attractive and simple conjecture, we deduce that $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking shares the common origin with all $CP$ violations. We study the common origin of $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ and $CP$ breaking in the Dirac mass matrix of seesaw Lagrangian (with right-handed neutrinos being $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ blind), which uniquely leads to inverted mass ordering of light neutrinos. We then predict a very different correlation between the two small $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking observables ${\ensuremath{\theta}}_{13}\ensuremath{-}0\ifmmode^\circ\else\textdegree\fi{}$ and ${\ensuremath{\theta}}_{23}\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$, which can saturate the present experimental upper limit on ${\ensuremath{\theta}}_{13}$. This will be tested against our previous normal mass-ordering scheme by the ongoing oscillation experiments. We also analyze the correlations of ${\ensuremath{\theta}}_{13}$ with Jarlskog invariant and neutrinoless $\ensuremath{\beta}\ensuremath{\beta}$-decay observable. From the common origin of $CP$ and $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking in the neutrino seesaw, we establish a direct link between the low energy $CP$ violations and the cosmological $CP$ violation for baryon asymmetry. With these we further predict a lower bound on ${\ensuremath{\theta}}_{13}$, supporting the ongoing probes of ${\ensuremath{\theta}}_{13}$ at Daya Bay, Double Chooz, and RENO experiments. Finally, we analyze the general model-independent ${\mathbb{Z}}_{2}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ symmetry structure of the light neutrino sector, and map it into the seesaw sector, where one of the ${\mathbb{Z}}_{2}$'s corresponds to the $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ symmetry ${\mathbb{Z}}_{2}^{\ensuremath{\mu}\ensuremath{\tau}}$ and another the hidden symmetry ${\mathbb{Z}}_{2}^{s}$ (revealed in our previous work) which dictates the solar mixing angle ${\ensuremath{\theta}}_{12}$. We derive the physical consequences of this ${\mathbb{Z}}_{2}^{s}$ and its possible partial violation in the presence of $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking (with or without the neutrino seesaw), regarding the ${\ensuremath{\theta}}_{12}$ determination and the correlation between $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ breaking observables.