Prediction of the CP Phase ${\delta }_{CP}$ in the Neutrino Oscillation and an Axion-less Solution to the Strong CP Problem

Abstract

A model of the axion-less solution to the strong CP problem has been recently constructed based on the ${\mathbf{T}}^2/{\mathbb{Z}}_3$ orbifold in the six dimensional space-time. We extend, in this paper, the model to include the lepton sector with three right-handed neutrinos. A crucial point in the extended model is that we have only one CP-violating phase and thus the CP phase in the neutrino oscillation can be predicted by the CP phase in the CKM matrix. The CP phase ${\delta }_{CP}$ in the PMNS matrix is predicted as ${\delta }_{CP}\simeq 192^{\circ }-195^{\circ }$ which can be tested in the near future experiments. We also discuss the effective mass $m_{\beta \beta }$ responsible for the neutrino-less double beta decay of nucleus, which is predicted as $m_{\beta \beta }\simeq 8-11$\,meV. We consider the leptogenesis and confirm that our model generates the right sign of the baryon asymmetry if the first family right-handed neutrino is the lightest among the heavy right-handed neutrinos.

Comments: Abstract and Section 4 are changed