Spontaneous CP Violating Phase as the Phase in PMNS Matrix

TL;DR

This paper explores the connection between spontaneous CP violation in the Higgs potential and the CP phases in the PMNS and CKM matrices, analyzing implications for neutrino physics and rare decay processes.

Contribution

It proposes a framework linking spontaneous CP violation phases with observable CP phases in lepton and quark mixing matrices, providing testable predictions.

Findings

Constraints on neutrino mass matrix and CP violation parameters

Predictions for neutrinoless double beta decay effective mass

Different phase identification models lead to distinct rare decay signatures

Abstract

We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is therefore also fixed. The mass matrix for neutrinos is constrained leading to constraints on the Jarlskog CP violating parameter $J$, and the effective mass $<m_{\beta\beta}>$ for neutrinoless double beta decay. The Yukawa couplings are also constrained. Different ways of identifying the phases have different predictions for $\mu \to e e\bar e$ and $\tau \to l_1 l_2 \bar l_3$. Future experimental data can be used to distinguish different models.