Radiative generation of $\bigtriangleup m^2_{21}$ and $\theta_{13}$ in two-fold degenerate neutrino models

Abstract

We study the implications on an important result on radiative corrections (JM conjecture) which states that the solar mass scale $\bigtriangleup m^2_{21}$ corresponding to the large mixing angle (LMA) MSW solution of the solar neutrino problem, can be generated through radiative corrections in the minimal supersymmetric standard model (MSSM) if two of the neutrino masses having opposite CP parity, are assumed to be degenerate and have non-zero value of $U_{e3}$ at high energy scale. We show that the above conjecture can be derived when we take the static solution of mixing angles from the general solution of RGEs. If we consider the simultaneous running of the three neutrino mass eigenvalues and mixing angles, the above two-fold degenerate case $m_i=(m, -m, m')$ with $m'\neq 0$ and $U_{e3}=0$, can also generate through radiative corrections, the non-zero values of $\bigtriangleup m^2_{21}$ and $U_{e3}$ at low scale, which are consistent with the LMA MSW solution. Such generalisation of JM conjecture may have important implications for model buildings from general gauge symmetry.