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Radiative and Seesaw Threshold Corrections to the $S_3$ Symmetric Neutrino Mass Matrix

We systematically analyze the radiative corrections to the $S_3$ symmetric neutrino mass matrix at high energy scale, say the GUT scale, in the charged lepton basis. There are significant corrections to the neutrino parameters both in the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM) with large tan$β$, when the renormalization group evolution (RGE) and seesaw threshold effects are taken into consideration. We find that in the SM all three mixing angles and atmospheric mass squared difference are simultaneously obtained in their current 3$σ$ ranges at the electroweak scale. However, the solar mass squared difference is found to be larger than its allowed 3$σ$ range at the low scale in this case. There are significant contributions to neutrino masses and mixing angles in the MSSM with large tan$β$ from the RGEs even in the absence of seesaw threshold corrections. However, we find that the mass squared differences and the mixing angles are obtained in their current 3$σ$ ranges at low energy when the seesaw threshold effects are also taken into account in the MSSM with large tan$β$.