Majorana CP-violating Research Articles

Majorana phases and neutrino–antineutrino oscillations

If massive neutrinos are the Majorana particles, how to pin down the Majorana CP-violating phases will eventually become an unavoidable question relevant to the future neutrino experiments. I argue that a study of neutrino–antineutrino oscillations will greatly help in this regard, although the issue remains purely academic at present. In this talk I first derive the probabilities and CP-violating asymmetries of neutrino–antineutrino oscillations in the three-flavor framework, and then illustrate their properties in two special cases: the normal neutrino mass hierarchy with m1 = 0 and the inverted neutrino mass hierarchy with m3 = 0. I demonstrate the significant contributions of the Majorana phases to the CP-violating asymmetries, even in the absence of the Dirac phase.

Leptonic CP violation and leptogenesis

The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector, are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature — Dirac or Majorana — of massive neutrinos, are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the universe, are considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U, are briefly reviewed.

Generalised geometrical CP violation in a T ′ lepton flavour model

We analyse the interplay of generalised CP transformations and the non-Abelian discrete group T ′ and use the semi-direct product G f = T ′ ⋊H CP, as family symmetry acting in the lepton sector. The family symmetry is shown to be spontaneously broken in a geometrical manner. In the resulting flavour model, naturally small Majorana neutrino masses for the light active neutrinos are obtained through the type I see-saw mechanism. The known masses of the charged leptons, lepton mixing angles and the two neutrino mass squared differences are reproduced by the model with a good accuracy. The model allows for two neutrino mass spectra with normal ordering (NO) and one with inverted ordering (IO). For each of the three spectra the absolute scale of neutrino masses is predicted with relatively small uncertainty. The value of the Dirac CP violation (CPV) phase δ in the lepton mixing matrix is predicted to be δ = π/2 or 3π/2. Thus, the CP violating effects in neutrino oscillations are predicted to be maximal (given the values of the neutrino mixing angles) and experimentally observable. We present also predictions for the sum of the neutrino masses, for the Majorana CPV phases and for the effective Majorana mass in neutrinoless double beta decay. The predictions of the model can be tested in a variety of ongoing and future planned neutrino experiments.

MajoranaCP-violating phases in neutrino-antineutrino oscillations and other lepton-number-violating processes

If the massive neutrinos are identified to be the Majorana particles via a convincing measurement of the neutrinoless double beta (0\nu\beta\beta) decay, how to determine the Majorana CP-violating phases in the 3 x 3 lepton flavor mixing matrix U will become a desirable experimental question. The answer to this question is to explore all the possible lepton-number-violating (LNV) processes in which the Majorana phases really matter. In this paper we carry out a systematic study of CP violation in neutrino-antineutrino oscillations, whose CP-conserving parts involve six independent 0\nu\beta\beta-like mass terms <m>_{\alpha\beta} and CP-violating parts are associated with nine independent Jarlskog-like parameters V^{ij}_{\alpha\beta} (for \alpha, \beta = e, \mu, \tau and i, j = 1, 2,3). With the help of current neutrino oscillation data, we analyze the sensitivities of |<m>_{\alpha\beta}| and V^{ij}_{\alpha\beta} to the three CP-violating phases of U, and illustrate the salient features of six independent CP-violating asymmetries between \nu_\alpha \to \bar{\nu}_\beta and \bar{\nu}_\alpha \to \nu_\beta oscillations. As a by-product, the effects of the CP-violating phases on the LNV decays of doubly- and singly-charged Higgs bosons are reexamined by taking account of the unsuppressed value of \theta_{13}. Such CP-conserving LNV processes can be complementary to the possible measurements of neutrino-antineutrino oscillations in the distant future.

Double Beta Decay Experiments: Beginning of a New Era

Interest in neutrinoless double beta decay (0νββ) has seen a significant renewal in the recent 10 years after evidence for neutrino oscillations was obtained from the results of atmospheric, solar, reactor, and accelerator neutrino experiments. These results are impressive proof that neutrinos have a nonzero mass. The detection and study of 0νββ decay may clarify the following problems of neutrino physics: (i) lepton number non-conservation, (ii) neutrino nature: whether the neutrino is a Dirac or a Majorana particle, (iii) absolute neutrino mass scale, (iv) the type of neutrino mass hierarchy (normal, inverted, or quasidegenerate), and (v) CP violation in the lepton sector (measurement of the Majorana CP-violating phases).

Properties ofCPviolation in neutrino-antineutrino oscillations

If the massive neutrinos are the Majorana particles, how to pin down the Majorana CP-violating phases will eventually become an unavoidable question relevant to the future neutrino experiments. We argue that a study of neutrino-antineutrino oscillations will greatly help in this regard, although the issue remains purely academic at present. In this work we first derive the probabilities and CP-violating asymmetries of neutrino-antineutrino oscillations in the three-flavor framework, and then illustrate their properties in two special cases: the normal neutrino mass hierarchy with m_1 = 0 and the inverted neutrino mass hierarchy with m_3 = 0. We demonstrate the significant contributions of the Majorana phases to the CP-violating asymmetries, even in the absence of the Dirac phase.

The Nature of Massive Neutrinos

The compelling experimental evidences for oscillations of solar, reactor, atmospheric, and accelerator neutrinos imply the existence of 3-neutrino mixing in the weak charged lepton current. The current data on the 3-neutrino mixing parameters are summarised and the phenomenology of 3-νmixing is reviewed. The properties of massive Majorana neutrinos and of their various possible couplings are discussed in detail. Two models of neutrino mass generation with massive Majorana neutrinos—the type I see-saw and the Higgs triplet model—are briefly reviewed. The problem of determining the nature, Dirac or Majorana, of massive neutrinos is considered. The predictions for the effective Majorana mass|〈m〉|in neutrinoless double-beta-((ββ)0ν-) decay in the case of 3-neutrino mixing and massive Majorana neutrinos are summarised. The physics potential of the experiments, searching for(ββ)0ν-decay for providing information on the type of the neutrino mass spectrum, on the absolute scale of neutrino masses, and on the Majorana CP-violation phases in the PMNS neutrino mixing matrix, is also briefly discussed. The opened questions and the main goals of future research in the field of neutrino physics are outlined.

Generalized scaling ansatz and minimal seesaw mechanism

Generalized scaling in flavor neutrino masses ${M}_{ij}$ ($i$, $j=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$) expressed in terms of ${\ensuremath{\theta}}_{\mathrm{SC}}$ and the atmospheric neutrino mixing angle ${\ensuremath{\theta}}_{23}$ is defined by ${M}_{i\ensuremath{\tau}}/{M}_{i\ensuremath{\mu}}=\ensuremath{-}{\ensuremath{\kappa}}_{i}{t}_{23}$ ($i=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$) with ${\ensuremath{\kappa}}_{e}=1$, ${\ensuremath{\kappa}}_{\ensuremath{\mu}}=B/A$ and ${\ensuremath{\kappa}}_{\ensuremath{\tau}}=1/B$, where ${t}_{23}=\mathrm{tan}{\ensuremath{\theta}}_{23}$, $A={cos}^{2}{\ensuremath{\theta}}_{\mathrm{SC}}+{sin}^{2}{\ensuremath{\theta}}_{\mathrm{SC}}{t}_{23}^{4}$ and $B={cos}^{2}{\ensuremath{\theta}}_{\mathrm{SC}}\ensuremath{-}{sin}^{2}{\ensuremath{\theta}}_{\mathrm{SC}}{t}_{23}^{2}$. The generalized scaling ansatz predicts the vanishing reactor neutrino mixing angle ${\ensuremath{\theta}}_{13}=0$. It is shown that the minimal seesaw mechanism naturally implements our scaling ansatz. There are textures satisfying the generalized scaling ansatz that yield vanishing baryon asymmetry of the Universe (BAU). Focusing on these textures, we discuss effects of ${\ensuremath{\theta}}_{13}\ensuremath{\ne}0$ to evaluate a $CP$-violating Dirac phase $\ensuremath{\delta}$ and BAU and find that BAU is approximately controlled by the factor ${sin}^{2}{\ensuremath{\theta}}_{13}\mathrm{sin}(2\ensuremath{\delta}\ensuremath{-}\ensuremath{\phi})$, where $\ensuremath{\phi}$ stands for the $CP$-violating Majorana phase whose magnitude turns out to be at most 0.1.

Phases of flavor neutrino masses and CP-violation

For flavor neutrino masses MijPDG (i,j=e,μ,τ) compatible with the phase convention defined by Particle Data Group (PDG), if neutrino mixings are controlled by small corrections to those with sinθ13=0 denoted by sinθ13δMeτPDG and sinθ13δMττPDG, CP-violating Dirac phase δCP is calculated to be δCP≈arg[(MμτPDG⁎/tanθ23+MμμPDG⁎)δMeτPDG+MeePDGδMeτPDG⁎−tanθ23MeμPDGδMττPDG⁎] (mod π), where θij (i,j=1,2,3) denotes an i–j neutrino mixing angle. If possible neutrino mass hierarchies are taken into account, the main source of δCP turns out to be δMeτPDG except for the inverted mass hierarchy with m˜1≈−m˜2, where m˜i=mie−iφi (i=1,2) stands for a neutrino mass mi accompanied by a Majorana phase φi for φ1,2,3 giving two CP-violating Majorana phases. We can further derive that δCP≈arg(MeμPDG)−arg(MμμPDG) with arg(MeμPDG)≈arg(MeτPDG) for the normal mass hierarchy and δCP≈arg(MeePDG)−arg(MeτPDG)+π for the inverted mass hierarchy with m˜1≈m˜2. For specific flavor neutrino masses Mij whose phases arise from Meμ,eτ,ττ, these phases can be connected with arg(MijPDG) (i,j=e,μ,τ). As a result, numerical analysis suggests that Dirac CP-violation becomes maximal as |arg(Meμ)| approaches to π/2 for the inverted mass hierarchy with m˜1≈m˜2 and for the degenerate mass pattern satisfying the inverted mass ordering and that Majorana CP-violation becomes maximal as |arg(Mττ)| approaches to its maximal value around 0.5 for the normal mass hierarchy. Alternative CP-violation induced by three CP-violating Dirac phases is compared with the conventional one induced by δCP and two CP-violating Majorana phases.

Vanishing effective mass of the neutrinoless double beta decay including light sterile neutrinos

Light sterile neutrinos with masses at the sub-eV or eV scale are hinted by current experimental and cosmological data. Assuming the Majorana nature of these hypothetical particles, we discuss their effects in the neutrinoless double beta decay by exploring the implications of a vanishing effective Majorana neutrino mass 〈m〉ee. Allowed ranges of neutrino masses, mixing angles and Majorana CP-violating phases are illustrated in some instructive cases for both normal and inverted mass hierarchies of three active neutrinos.

Higgs triplets at like-sign linear colliders and neutrino mixing

We study the phenomenology of the type-II seesaw model at a linear e^-e^- collider. We show that the process e^-e^- \rightarrow alpha^-beta^- (alpha, beta = e, mu, tau being charged leptons) mediated by a doubly charged scalar is very sensitive to the neutrino parameters, in particular the absolute neutrino mass scale and the Majorana CP-violating phases. We identify the regions in parameter space in which appreciable collider signatures in the channel with two like-sign muons in the final state are possible. This includes Higgs triplet masses beyond the reach of the LHC.

Finite quantum corrections to the tribimaximal neutrino mixing

We calculate finite quantum corrections to the tribimaximal neutrino mixing pattern VTB in three generic classes of neutrino mass models. We show that three flavor mixing angles can all depart from their tree-level results described by VTB, among which θ12 is most sensitive to such quantum effects, and the Dirac CP-violating phase can radiatively arise from two Majorana CP-violating phases. This theoretical scheme offers a new way to understand why θ13 is naturally small and how three CP-violating phases are presumably correlated.

NEUTRINO MIXING, LEPTONIC CP VIOLATION, THE SEESAW MECHANISM AND BEYOND

The phenomenology of 3-neutrino mixing and of the related Dirac and Majorana leptonic CP violation is reviewed. The leptogenesis scenario of generation of the baryon asymmetry of the Universe, which is based on the see-saw mechanism of neutrino mass generation, is considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U are briefly reviewed.

Lepton-number-violating decays of singly-charged Higgs bosons in the type-(I + II) seesaw model

The lepton-number-violating decays of singly-charged Higgs bosons H± are investigated in the minimal type-(I + II) seesaw model with one SU(2)L Higgs triplet Δ and one heavy Majorana neutrino N1 at the TeV scale. We find that the branching ratios B(H+ → lα+ν̄) (for α = e,μ,τ) depend not only on the mass and mixing parameters of three light neutrinos νi (for i = 1,2,3) but also on those of N1. Assuming that the mass of N1 lies in the range of 200 GeV to 1 TeV, we figure out the generous interference bands for the contributions of νi and N1 to B(H+ → lα+ν̄). We illustrate some salient features of such interference effects by considering three typical mass patterns of νi, and show that the relevant Majorana CP-violating phases can affect the magnitudes of B(H+ → lα+ν̄) in this parameter region.

Majorana CP Violation in Approximately - Symmetric Models with det(M ) = 0

We discuss effects of Majorana CP violation in a model-independent way for a given phase structure of flavor neutrino masses. To be more predictive, we confine ourselves to models with $\det(M_\nu)=0$, where $M_\nu$ is a flavor neutrino mass matrix, and to be consistent with observed results of the neutrino oscillation, the models are subject to an approximate $\mu$-$\tau$ symmetry. There are two categories of approximately $\mu$-$\tau$ symmetric models classified as (C1) yielding $\sin^22\theta_{23} \approx 1$ and $\sin^2\theta_{13} \ll 1$ and (C2) yielding $\sin^22\theta_{23} \approx 1$ and $\Delta m_\odot^2/|\Delta m_{atm}^2|\ll 1$, where $\theta_{23(13)}$ stands for the mixing of massive neutrinos $\nu_2$ and $\nu_3$ ($\nu_1$ and $\nu_3$) and $\Delta m_ \odot ^2$ ($\Delta m_{atm}^2$) stands for the mass squared difference for atmospheric (solar) neutrinos. The Majorana phase can be large for the normal mass hierarchy and for the inverted mass hierarchy with $m_1\approx -m_2$ only realized in (C1) while they are generically small for the inverted mass hierarchy with $m_1\approx m_2$ in both (C1) and (C2). These results do not depend on a specific choice of phases in $M_\nu$ but hold true in any models with $\det(M_\nu)=0$ because of the rephasing invariance.

Majorana phases and leptogenesis in see-saw models withA4symmetry

The related issues of Majorana CP violation in the lepton sector and leptogenesis are investigated in detail in two rather generic supersymmetric models with type I see-saw mechanism of neutrino mass generation and A_4 flavour symmetry, which naturally lead at leading order to tri-bimaximal neutrino mixing. The neutrino sector in this class of models is described at leading order by just two real parameters and one phase. This leads, in particular, to significant low energy constraints on the Majorana phases \alpha_{21} and \alpha_{31} in the PMNS matrix, which play the role of leptogenesis CP violating parameters in the generation of the baryon asymmetry of the Universe. We find that it is possible to generate the correct size and sign of the baryon asymmetry in both A_4 models. The sign of the baryon asymmetry is directly related to the signs of sin\alpha_{21} and/or sin\alpha_{31}.

Concluding remarks: Neutrino mixing, Majorana CP-violation, (ββ)0v,-decay and Beyond

The problem of determination of the nature - Dirac or Majorana, of massive neutrinos is discussed. The physics potential of experiments, searching for (ββ)0v-decay, for providing information on the type of v-mass spectrum, absolute scale of v- masses and on the Majorana CP-violating phases in the PMNS neutrino mixing matrix U, is reviewed. The possibility that the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Majorana CP-violating phase(s) in U, is also briefly discussed.

Dirac and Majorana leptonic CP-violation and leptogenesis

We briefly review the results showing that the CP-violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis with ‘hierarchical’ heavy Majorana neutrinos can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U. One can have successful leptogenesis, in particular, even if the only source of CP-violation is the Dirac phase δ in U. For light ν-mass spectrum with normal (inverted) hierarchy, this requires |sin θ13 sinδ| ≥ 0.09 (0.02), θ13 being the CHOOZ angle.

Leptogenesis and low energy CP-violation in neutrino physics

Taking into account the recent progress in the understanding of the lepton flavor effects in leptogenesis, we investigate in detail the possibility that the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Dirac and/or Majorana CP-violating phases in the PMNS neutrino mixing matrix U, and thus is directly related to the low energy CP-violation in the lepton sector (e.g., in neutrino oscillations, etc.). We first derive the conditions of CP-invariance of the neutrino Yukawa couplings λ in the see-saw Lagrangian, and of the complex orthogonal matrix R in the “orthogonal” parametrization of λ. We show, e.g. that under certain conditions (i) real R and specific CP-conserving values of the Majorana and Dirac phases can imply CP-violation, and (ii) purely imaginary R does not necessarily imply breaking of CP-symmetry. We study in detail the case of hierarchical heavy Majorana neutrino mass spectrum, presenting results for three possible types of light neutrino mass spectrum: (i) normal hierarchical, (ii) inverted hierarchical, and (iii) quasi-degenerate. Results in the alternative case of quasi-degenerate in mass heavy Majorana neutrinos, are also derived. The minimal supersymmetric extension of the standard theory with right-handed Majorana neutrinos and see-saw mechanism of neutrino mass generation is discussed as well. We illustrate the possible correlations between the baryon asymmetry of the Universe and (i) the rephasing invariant J CP controlling the magnitude of CP-violation in neutrino oscillations, or (ii) the effective Majorana mass in neutrinoless double beta decay, in the cases when the only source of CP-violation is respectively the Dirac or the Majorana phases in the neutrino mixing matrix.

Neutrinos as a probe of CP-violation and leptogenesis

Establishing CP-violation in the lepton sector is one of the most challenging future tasks in neutrino physics. The lepton mixing matrix contains one Dirac phase and, if neutrinos are Majorana particles, two additional CP-violating phases. I will review the main theoretical aspects of CP-violation in the lepton sector. Then, I will present the strategies for determining the Dirac and the Majorana CP-violating phases in long-baseline and neutrinoless double beta decay experiments, respectively. Leptonic CP-violation has received recently a lot of attention as it might be at the origin of the baryon asymmetry of the Universe. Within the context of the see-saw mechanism, I will discuss the possible connection between the CP-violating phases measurable at low energy with the ones entering in leptogenesis.