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