Radiatively broken symmetries of nonhierarchical neutrinos

Abstract

Symmetry-based ideas, such as the quark-lepton complementarity principle and the tribimaximal mixing scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale Λ~10¹² GeV characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalization group evolution down to a laboratory energy scale λ~10³ GeV tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases α_2,3 enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the minimal supersymmetric standard model and demonstrate the fact posited above for two versions of quark-lepton complementarity and two versions of tribimaximal mixing. The appropriate constraints are worked out for all these four cases. Specifically, a preference for α₂≈ p (i.e., m₁≈−m₂) emerges in each case. We also show how a future accurate measurement of θ₁₃ may enable some discrimination among these four cases in spite of renormalization group evolution.