Radiative Generation of $\theta_{13}$ with the Seesaw Threshold Effect

We examine whether an appreciable value of the lepton flavor mixing angle $\theta_{13}$ at the electroweak scale $\Lambda_{\rm EW}$ can be radiatively generated from $\theta_{13} = 0^\circ$ at the GUT scale $\Lambda_{\rm GUT}$. It is found that the renormalization-group running and seesaw threshold effects may lead to $\theta_{13} \sim 5^\circ$ at low energies for two simple large-maximal mixing patterns of the MNS matrix in the minimal supersymmetric standard model. If $\theta_{12}$ is sufficiently large at $\Lambda_{\rm GUT}$, it will be possible to radiatively produce $\theta_{13} \sim 5^\circ$ at $\Lambda_{\rm EW}$ both in the standard model and in its supersymmetric extensions. The mass spectrum of three heavy right-handed Majorana neutrinos and the cosmological baryon number asymmetry via leptogenesis are also calculated.