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

TL;DR

This paper extends a six-dimensional orbifold model solving the strong CP problem without axions to include leptons, predicting the neutrino CP phase and effective mass for neutrinoless double beta decay, with implications for baryogenesis.

Contribution

The paper introduces an extended model incorporating the lepton sector with a single CP-violating phase, predicting the neutrino CP phase and effective mass, linking it to baryon asymmetry generation.

Findings

Predicted neutrino CP phase $oxed{ ot= 180^ ext{o}}$, approximately 192°-195°.

Estimated effective mass $m_{etaeta} oughly 8-11$ meV for neutrinoless double beta decay.

Confirmed leptogenesis can produce the correct baryon asymmetry with specific neutrino mass hierarchy.

Abstract

A model of the axion-less solution to the strong CP problem has been recently constructed based on the $\bf T^2/\mathbb{Z}_3$ 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.