Majorana CP phases in bi-pair neutrino mixing and leptogenesis

TL;DR

This paper estimates Majorana CP phases within bi-pair neutrino mixing, explores their role in leptogenesis, and finds specific phase ranges consistent with observed baryon asymmetry and neutrino mixing angles.

Contribution

It provides a novel analysis of Majorana CP phases in bi-pair neutrino mixing and their implications for leptogenesis within the minimal seesaw model.

Findings

Majorana CP phase  is between 0.69 and 0.92 radians.

Phases  and  are approximately 0.31 to 0.40 radians and -1.25 to -0.32 radians.

The phases satisfy a numerical relation |\u001c|\u2248 2||.

Abstract

We estimate Majorana CP phases for a given flavor neutrino mass matrix (M_\nu) consistent with the bi-pair neutrino mixing, which is recently proposed to describe neutrino mixings given by \sin\theta_{13}=0 for the reactor neutrino mixing, \sin^2\theta_{12} = 1-1/\sqrt{2} for the solar neutrino mixing and either \sin^2\theta_{23} = \tan^2\theta_{12} or \sin^2\theta_{23}=1-\tan^2\theta_{12} for the atmospheric neutrino mixing. Sizes of Majorana CP phases are evaluated so as to generate the observed baryon asymmetry in the universe via a leptogenesis scenario within the framework of the minimal seesaw model, where M_\nu satisfies det(M_\nu)=0 and one active Majorana CP phase (\phi) is present. Assuming the normal mass hierarchy for light neutrinos and one zero texture for a 3X2 Dirac neutrino mass matrix, we find that \phi lies in the region of 0.69<|\phi|<0.92 [rad], which is converted into allowed regions of \alpha=arg(M_{e\mu}) and \beta=arg(M_{e\tau}), where M_{ij} (i,j=e,\mu,\tau) denote the i-j matrix element of M_\nu. The phases \alpha and \beta turn out to satisfy 0.31<|\alpha|<0.40 [rad] and -1.25<\beta<-0.32 [rad]. The approximate numerical equality of |\phi|\approx 2|\alpha| is consistent with our theoretical estimation of \phi=\phi_2-\phi_3 for \phi_2=-(\alpha+\beta) and \phi_3\approx \alpha-\beta valid for the normal mass hierarchy. We also find the following scaling property: (M'^{\mu\mu}-M'^{ee}/t^2_{12})/M'^{\mu\tau}=M'^{\mu\tau}/(M'^{\tau\tau}-M'^{ee}/t^2_{12})=-M'^{e\tau}/M'^{e\mu} (t^2_{12}=\tan^2\theta_{12}=\sqrt{2}-1), where M'^{ij} stands for M_{ij} evaluated on the basis of the Particle Data Group's phase convention.