Impacts of the observedθ13on the running behaviors of Dirac and Majorana neutrino mixing angles andCP-violating 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.