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

Abstract

We examine whether an appreciable value of the lepton flavor mixing angle $θ_{13}$ at the electroweak scale $Λ_{\rm EW}$ can be radiatively generated from $θ_{13} = 0^\circ$ at the GUT scale $Λ_{\rm GUT}$. It is found that the renormalization-group running and seesaw threshold effects may lead to $θ_{13} \sim 5^\circ$ at low energies for two simple large-maximal mixing patterns of the MNS matrix in the minimal supersymmetric standard model. If $θ_{12}$ is sufficiently large at $Λ_{\rm GUT}$, it will be possible to radiatively produce $θ_{13} \sim 5^\circ$ at $Λ_{\rm EW}$ 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.