Generalized Tri-bimaximal Neutrino Mixing and Its Sensitivity to Radiative Corrections

Abstract

We argue that the tri-bimaximal neutrino mixing pattern $V_0$ or its generalized form $V_0^{\prime }$, which includes two arbitrary Majorana phases of CP violation, may result from an underlying flavor symmetry at a superhigh energy scale close to the seesaw scale ($\sim 10^{14}$ GeV). Taking the working assumption that three neutrino masses are nearly degenerate, we calculate radiative corrections to $V_0$ and $V_0^{\prime }$ in their evolution down to the electroweak scale ($\sim 10^2$ GeV). Three mixing angles of $V_0$ or $V_0^{\prime }$ are essentially stable against radiative corrections in the standard model (SM). In the minimal supersymmetric standard model (MSSM), however, $V_0$ is in general disfavored and $V_0^{\prime }$ can be compatible with current neutrino oscillation data if its two Majorana phases ${\alpha }_1^{}$ and ${\alpha }_2^{}$ are properly fine-tuned. We also find that it is possible to radiatively generate the CP-violating phase $\delta$ from ${\alpha }_1^{}$ and ${\alpha }_2^{}$, and \delta may keep on staying at its fixed point in either the SM or the MSSM.

Comments: RevTex 14 pages, 2 figures. Table I corrected. Minor changes made. More discussions added