The issue of existence of Majorana neutrinos with masses of the order of TeV and substantial couplings is addressed. A general neutrino mass matrix $M_{ \nu}$ with both features is constructed, however, the form of $M_{ \nu}$ is constrained very much by severe relations among the elements of $m_D$ and $M_R$ submatrices of $M_{ \nu}$. These general relations follow from the perturbative construction of the light neutrino mass spectrum. To avoid such large correlations between low mass parameters in $m_D$ and large mass parameters in $M_R$, the Je\.zabek-Sumino see-saw model of bi-maximal neutrino mixing adopted to the TeV scale and the issue of possible symmetries of the matrix $M_{ \nu}$ are discussed. Results are supported by a few numerical examples which show directly the complexity of the problem.
Categories: hep-ph