Neutrino symmetries from high to low scales

Abstract

Proposed symmetry relations, e.g., quark-lepton complementarity (QLC) or tribimaximal mixing (TBM), need to be imposed at a high scale $\wedge \sim 10^{12}$ GeV characterising the large masses of right-handed neutrinos required to implement the seesaw mechanism. RG evolution down to the laboratory scale $\lambda \sim 10^3$ GeV, generically prone to spoil these relations and their predicted neutrino mixing patterns, can be made to preserve them by appropriately constraining the Majorana phases $\alpha_{2,3}$. This is explicitly demonstrated in the MSSM for two versions of QLC and two versions of TBM. A preference for $\alpha_2 \simeq \pi$ (i.e. $m_1 \simeq - m_2$) emerges in each case. Discrimination among the four cases is shown to be possible by future measurements of $\theta_{13}$.