Impacts of the observed theta_{13} on the running behaviors of Dirac and Majorana neutrino mixing angles and CP-violating phases

TL;DR

This paper investigates how the observed neutrino mixing angle θ13 influences the evolution of neutrino mixing parameters and CP phases from high to low energy scales within the MSSM framework, highlighting the role of CP phases.

Contribution

It demonstrates that a sizable θ13 at high energy can evolve to observed values at low energy, emphasizing the importance of CP phases in this process within the MSSM.

Findings

Large θ13 can be generated from zero at high scale via radiative corrections.

CP-violating phases significantly affect the evolution of mixing angles.

Radiative corrections to mixing angles are small but comparable, depending on phases.

Abstract

The recent observation of the smallest neutrino mixing angle $\theta_{13}$ in the Daya Bay and RENO experiments motivates us to examine whether $\theta_{13} \simeq 9^\circ$ at the electroweak scale can be generated from $\theta_{13} = 0^\circ$ at a superhigh-energy scale via the radiative corrections. We find that it is difficult but not impossible in the minimal supersymmetric standard model (MSSM), and a relatively large $\theta_{13}$ may have some nontrivial impacts on the running behaviors of the other two mixing angles and CP-violating phases. In particular, we demonstrate that the CP-violating phases play a crucial role in the evolution of the mixing angles by using the one-loop renormalization-group equations of the Dirac or Majorana neutrinos in the MSSM. We also take the "correlative" neutrino mixing pattern with $\theta_{12} \simeq 35.3^\circ$, $\theta_{23} = 45^\circ$ and $\theta_{13} \simeq 9.7^\circ$ at a presumable flavor symmetry scale as an example to illustrate that the three mixing angles can receive comparably small radiative corrections and thus evolve to their best-fit values at the electroweak scale if the CP-violating phases are properly adjusted.