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

Abstract

We examine whether an appreciable value of the lepton flavor mixing angle ${\theta }_{13}$ at the electroweak scale ${\Lambda }_{\mathrm{EW}}$ can be radiatively generated from ${\theta }_{13}=0^{\circ }$ at the GUT scale ${\Lambda }_{\mathrm{GUT}}$. 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 ${\Lambda }_{\mathrm{GUT}}$, it will be possible to radiatively produce ${\theta }_{13}\sim 5^{\circ }$ at ${\Lambda }_{\mathrm{EW}}$ 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.

Comments: 13 pages, 1 table, 3 figures; text improved, more result added to the table, matching the version accepted for publication in PRD