CPViolation in Neutrino Oscillation and Leptogenesis

Abstract

We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant J as well as neutrinoless double β decay by identifying a low energy CP violating phase which signals the CP violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and J is obtained. For the most general case of the framework, we study the effect on J coming from the phases which are not related to leptogenesis, and also show how the correlation can be lost in the presence of those phases.PACS numbers: 11.30.e, 11.30.f, 14.60 p Finding any relation between baryogenesis via leptogenesis [1] and low energy CP violation observed in the laboratory is a very interesting issue [2]. The CP violation required for leptogenesis stems from the CP phases in the heavy Majorana sector, whereas CP violation measurable from the neutrino oscillations [3] can be described by the neutrino mixing matrix. One interesting question concerned with the low energy leptonic CP violation is whether it can be affected by the CP violating phases responsible for leptogenesis. Several people [4] have already discussed some potential connections between low energy CP violation and leptogenesis by using some ansatz, but it is still unclear how large the former can affect the latter in general. The major difficulty to quantify such a connection occurs due to lack of the available low energy data to fix parameters of the seesaw model.The purpose of this paper is to examine in a rather general framework how leptogenesis can be related to the low energy CP violation by determining the parameters as many as possible from available low energy experimental results and cosmological observations. In order to make a quantitative analysis of the connection between low energy leptonic CP violation and leptogenesis, we consider * E-mail:endoh@theo.phys.hiroshima-u.ac.jp † E-mail:kaneko@muse.sc.niigata-u.ac.jp ‡ E-mail:kang@theo.phys.hiroshima-u.ac.jp § E-mail:morozumi@theo.phys.sci.hiroshima-u.ac.jp * * E-mail:tanimoto@muse.sc.niigata-u.ac.jp the minimal CP violating seesaw model which has two heavy Majorana neutrinos and three light left-handed neutrinos; (3,2) seesaw model. As will be shown later, to break CP symmetry, the required minimal number of singlet heavy Majorana neutrino is two in the seesaw model with three light lepton doublets. This (3,2) seesaw model is consistent with recent data of neutrino oscillations and contains 8 real parameters and 3 CP violating phases in the neutrino sectors which make this model more constrained and predictive compared with the general (3,3) seesaw model [5] with 18 parameters. We will show that while all three CP violating phases contribute to low energy leptonic CP violation, only a single CP violating...

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“…Consider the minimal 3 × 2 see-saw model [12,13], which contains only 2 heavy Majorana neutrinos. This model has altogether 11 parameters, 8 real and 3 CP violating phases.…”

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