Renormalization group evolution of neutrino mixing parameters near θ₁₃=0 and models with vanishing θ₁₃ at the high scale

Abstract

Renormalization group (RG) evolution of the neutrino mass matrix may take the value of the mixing angle θ₁₃ very close to zero, or make it vanish. On the other hand, starting from θ₁₃=0 at the high scale it may be possible to generate a nonzero θ₁₃, radiatively. In the most general scenario with nonvanishing CP violating Dirac and Majorana phases, we explore the evolution in the vicinity of θ₁₃=0, in terms of its structure in the complex U_ε3 plane. This allows us to explain the apparent singularity in the evolution of the Dirac CP phase δ at θ₁₃=0. We also introduce a formalism for calculating the RG evolution of neutrino parameters that uses the Jarlskog invariant and naturally avoids this singular behavior. We find that the parameters need to be extremely fine-tuned in order to get exactly vanishing θ₁₃ during evolution. For the class of neutrino mass models with θ₁₃=0 at the high scale, we calculate the extent to which RG evolution can generate a nonzero θ₁₃, when the low energy effective theory is the standard model or its minimal supersymmetric extension. We find correlated constraints on θ₁₃, the lightest neutrino mass m₀, the effective Majorana mass m_εε measured in the neutrinoless double beta decay, and the supersymmetric parameter tanβ.