Generalized Scaling Ansatz and Minimal Seesaw Mechanism

TL;DR

This paper introduces a generalized scaling ansatz for neutrino masses, shows its natural implementation in the minimal seesaw mechanism, and explores implications for baryon asymmetry and CP violation, especially considering nonzero $ heta_{13}$.

Contribution

It proposes a new generalized scaling ansatz for neutrino masses and demonstrates its realization within the minimal seesaw framework, linking it to baryon asymmetry and CP violation.

Findings

The generalized scaling ansatz predicts $ heta_{13}=0$ in its original form.

Textures satisfying the ansatz can lead to zero baryon asymmetry.

Effects of nonzero $ heta_{13}$ on CP phase and BAU are quantitatively analyzed.

Abstract

Generalized scaling in flavor neutrino masses $M_{ij}$ ($i,j$=$e,\mu,\tau$) expressed in terms of $\theta_{SC}$ and the atmospheric neutrino mixing angle $\theta_{23}$ is defined by $M_{i\tau}/M_{i\mu}$ = $- \kappa_it_{23}$ ($i$=$e,\mu,\tau$) with $\kappa_e$=1, $\kappa_\mu$=B/A and $\kappa_\tau$=1/B, where $t_{23}=\tan\theta_{23}$, $A$=${\cos ^2}{\theta_{SC}}+{\sin ^2}{\theta_{SC}}t_{23}^4$ and B=${\cos ^2}{\theta_{SC}}-{\sin ^2}{\theta_{SC}}t_{23}^2$. The generalized scaling ansatz predicts the vanishing reactor neutrino mixing angle $\theta_{13}=0$. It is shown that the minimal seesaw mechanism naturally implements our scaling ansatz. There are textures satisfying the generalized scaling ansatz that yield vanishing baryon asymmetry of the Universe (BAU). Focusing on these textures, we discuss effects of $\theta_{13}\neq 0$ to evaluate a CP-violating Dirac phase $\delta$ and BAU and find that BAU is approximately controlled by the factor $\sin^2\theta_{13}\sin(2\delta -\phi)$, where $\phi$ stands for the CP-violating Majorana phase whose magnitude turns out to be at most 0.1.