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Scaling in flavor neutrino masses $M_{ij}$ ($i,j$=$e,\mu,\tau$) can bedescribed by two angles: $\theta_{SC}$ and the atmospheric neutrino mixingangle $\theta_{23}$. 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 ansatzdictates 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 vanishingreactor neutrino mixing angle $\theta_{13}=0$. This generalized scaling isnaturally realized in seesaw textures. To obtain $\theta_{13}\neq 0$ asrequired by the recent experimental results, we introduce breaking terms ofscaling 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 thatconnect CP violating phases with phases of flavor neutrino masses, which arefound 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 observedis 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) masshierarchy.

Generalized Scaling in Flavor Neutrino Masses