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Generalized Scaling Ansatz and Minimal Seesaw Mechanism

published in Phys. Rev. D 86 No.11 (2012) 116011 1-9 (Received date: November, 2012).

$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 anzatz predicts the vanishing reactor neutrino mixing angle $\theta_{13}=0$. It is shown that the minimal seesaw mechanism naturally implements our scaling anzatz. There are textures satisfying the generalized scaling anzatz that yield vanishing baryon asymmetry of the Universe (BAU). Focusing on these textures, we discuss effects of $\theta_{13}\neq 0$ to evaluate 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.$

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