Renormalization group evolution of neutrino mixing parameters near $\theta_{13} = 0$ and models with vanishing $\theta_{13}$ at the high scale

TL;DR

This paper investigates how neutrino mixing angles, especially _{13}, evolve under renormalization group effects near zero, exploring the conditions for generating or maintaining a vanishing _{13} in different models.

Contribution

It introduces a formalism for RG evolution of neutrino parameters that avoids singularities at _{13}=0 and analyzes the fine-tuning needed for _{13} to remain zero during evolution.

Findings

RG evolution can generate non-zero _{13} in models with _{13}=0 at high scale.

Exact _{13}=0 requires extreme fine-tuning during RG evolution.

Constraints relate _{13}, lightest neutrino mass, neutrinoless double beta decay, and .

Abstract

Renormalization group (RG) evolution of the neutrino mass matrix may take the value of the mixing angle $\theta_{13}$ very close to zero, or make it vanish. On the other hand, starting from $\theta_{13}=0$ at the high scale it may be possible to generate a non-zero $\theta_{13}$ radiatively. In the most general scenario with non-vanishing CP violating Dirac and Majorana phases, we explore the evolution in the vicinity of $\theta_{13}=0$, in terms of its structure in the complex ${\cal U}_{e3}$ plane. This allows us to explain the apparent singularity in the evolution of the Dirac CP phase $\delta$ at $\theta_{13}=0$. We also introduce a formalism for calculating the RG evolution of neutrino parameters that uses the Jarlskog invariant and naturally avoids this singular behaviour. We find that the parameters need to be extremely fine-tuned in order to get exactly vanishing $\theta_{13}$ during evolution. For the class of neutrino mass models with $\theta_{13}=0$ at the high scale, we calculate the extent to which RG evolution can generate a nonzero $\theta_{13}$, when the low energy effective theory is the standard model or its minimal supersymmetric extension. We find correlated constraints on $\theta_{13}$, the lightest neutrino mass $m_0$, the effective Majorana mass $m_{ee}$ measured in the neutrinoless double beta decay, and the supersymmetric parameter $\tan\beta$.