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_e3 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 meemeasured in the neutrinoless double beta decay and the supersymmetric parameter tan β.