Abstract
We show that in see-saw models with small or even vanishing lepton mixing angle $\theta_{12}$, maximal $\theta_{23}$, zero $\theta_{13}$ and zero CP phases at the GUT scale, the currently favored LMA solution of the solar neutrino problem can be obtained in a rather natural way by Renormalization Group effects. We find that most of the running takes place in the energy ranges above and between the see-saw scales, unless the charged lepton Yukawa couplings are large, which would correspond to a large $\tan \beta$ in the Minimal Supersymmetric Standard Model (MSSM). The Renormalization Group evolution of the solar mixing angle $\theta_{12}$ is generically larger than the evolution of $\theta_{13}$ and $\theta_{23}$. A large enhancement occurs for an inverted mass hierarchy and for a regular mass hierarchy with $|m_2 - m_1| \ll |m_2 + m_1|$. We present numerical examples of the evolution of the lepton mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the LMA mixing angles are produced with vanishing solar mixing angle $\theta_{12}$ at the GUT scale.
Highlights
The relevant RGE’s were derived in [23]–[28]
In a recent study [29], we showed that starting with bimaximal mixing at the GUT scale, the large solar mixing of the LMA solution can be explained as an effect of the RG evolution of the mixing angles
We have studied the RG evolution of the lepton mixing angles in see-saw scenarios in the SM and in the Minimal Supersymmetric Standard Model (MSSM)
Summary
To evolve the lepton mixing angles and neutrino masses from the GUT scale to the electroweak (EW) or Supersymmetry (SUSY)-breaking scale in a see-saw model, a series of effective theories has to be used. These are obtained by successively integrating out the heavy singlets at their mass thresholds, which are non-degenerate in general. Starting at the GUT scale, the strategy is to solve the systems of coupled differential equations of the form μ d dμ (n). Due to the complicated structure of the set of differential equations, the exact solution can only be obtained numerically.
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