In this talk, we present a recent investigation of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos in terms of CP-odd weak-basis invariants. The number of weak-basis invariants to guarantee CP conservation in the leptonic sector is clarified and a new set of invariants are advocated for the description of CP conservation, given the physical parameters in their experimentally allowed regions.
The electric dipole moment of the electron, $d_e$, is known to vanish up to thre e-loops in the standard model with massless neutrinos. However, if neutrinos are massive Majorana particles, we obtain the result that $d_e$ induced by leptonic CKM mechanism is non-vanishing at two-loop order, and it applies to all massive Majorana neutrino models.
We relate the observed pattern of leptonic mixing to the quaidegeneracy of three Majorana neutrinos. We show how lifting the degeneracy may lead to the measured value of $|U_{13}|$ and to sizeable CP violation of Dirac-type. We show some of the correlations obtained among physical observables, starting from some of the most interesting schemes proposed in the literature.
B meson semi-leptonic rare decays are sensitive to new physics beyond standard model. We study the $B^{-}\to π^{-}μ^{+}μ^{-}$ process and investigate the Majorana neutrino contribution to its decay width. The constraints on the Majorana neutrino mass and mixing parameter are obtained from this decay channel with the latest LHCb data. Utilizing the best fit for the parameters, we study the lepton number violating decay $B^{-}\to π^{+}μ^{-}μ^{-}$, and find its branching ratio is about $6.4\times10^{-10}$, which is consistent with the LHCb data reported recently.
The notion of U(1) lepton number (which may only be softly broken) is applied to models of dark matter which interacts with leptons. Previous scotogenic models of Majorana or Dirac neutrino mass are shown to be derivable in this framework without additional symmetries. Only complete renormalizable theories are considered. An explicit class of models with $Z_n$ ($n \geq 5$) lepton and dark symmetry for Dirac neutrinos is derived, as well as an example of $Z_3$ dark symmetry.
We propose that the observed large leptonic mixing may just reflect a quasidegeneracy of three Majorana neutrinos. The limit of exact degeneracy of Majorana neutrinos is not trivial, as leptonic mixing and even CP violation may occur. We conjecture that the smallness of $|U_{13}|$, when compared to the other elements of $U_{PMNS}$, may just reflect the fact that, in the limit of exact mass degeneracy, the leptonic mixing matrix necessarily has a vanishing element. We show that the lifting of the mass degeneracy can lead to the measured value of $|U_{13}|$ while at the same time accommodating t…
In the Standard Model minimally extended to include massive neutrinos, we compute the leading CP-violating zero temperature contributions to the one-loop effective action induced by integration of the leptons. Such contributions start at operators of dimension six and they are P even for Dirac neutrinos and P even or odd for Majorana neutrinos. Dimension four operators are allowed in the mixed Dirac-Majorana case. It is verified by explicit calculation that CP can be violated in two generation settings for Majorana neutrinos. Using different neutrino scenarios we give upper bounds for the coup…
In the present paper, we carry out a systematic study of the flavor invariants and their renormalization-group equations (RGEs) in the leptonic sector with three generations of charged leptons and massive Majorana neutrinos. First, following the approach of the Hilbert series from the invariant theory, we show that there are 34 basic flavor invariants in the generating set, among which 19 invariants are CP-even and the others are CP-odd. Any flavor invariants can be expressed as the polynomials of those 34 basic invariants in the generating set. Second, we explicitly construct all the basic in…
We propose a strategy for distinguishing the Dirac / Majorana character of heavy neutrinos with masses below the $W$ boson mass, using purely leptonic decays at the LHC. The strategy makes use of a forward-backward asymmetry of the opposite charge lepton in the $W^{+}\rightarrow l^{+}l^{+}l^{'-}ν$ decay. In order to check the experimental feasibility of the model, we show, through a numerical analysis, that in the decay $W^{+}\rightarrow e^{+}e^{+}μ^{-}ν$ the two positrons in the final state can be distinguished for different ranges of the heavy neutrino masses. Finally, we estimated the numbe…
Minimal Flavour Violation can be realized in several ways in the lepton sector due to the possibility of Majorana neutrino mass terms. We derive the scalar potential for the fields whose background values are the Yukawa couplings, for the simplest See-Saw model with just two right-handed neutrinos, and explore its minima. The Majorana character plays a distinctive role: the minimum of the potential allows for large mixing angles -in contrast to the simplest quark case- and predicts a maximal Majorana phase. This points in turn to a strong correlation between neutrino mass hierarchy and mixing …
The neutrino masses and mixings indicated by current neutrino oscillation experiments suggest that the neutrino mass matrix possesses an approximate $μ-τ$ exchange symmetry. In this study, we explore the neutrino parameter space and show that if a small $μ-τ$ symmetry breaking is considered, the Majorana $CP$ phases must be unequal and non-zero independently of the neutrino mass scale. Moreover, a small $μ-τ$ symmetry breaking favors quasi-degenerate masses. We also show that Majorana phases are strongly correlated with the Dirac $CP$ violating phase. Within this framework, we obtain robust pr…
In the preprint arXiv:2110.08210, some comments on our paper recently published in JHEP \textbf{09} (2021) 053 have been made. Since some of the comments are completely wrong and others are quite misleading, we decide to clarify the relevant issues in a formal reply. First of all, nothing is wrong about our calculations and physical results in the original paper. Second, there is no logical gap to fill at all. The fact that the $N$-dimensional unitary group over the field of complex numbers ${\rm U}(N,\mathbb{C})$ is not a linear algebraic group is actually irrelevant for the validity of the M…
I study, in the leptonic sector, the role of the $SU(2)_V$ custodial symmetry $\ti{\cal G}$ which was shown in ref. [1] to control the quantization of the electric charge in the $J=0$ mesonic sector. The electroweak theory is considered, according to ref. [2], as a purely vectorial model which interacts with a ``hidden'' sector of composite scalars. $\ti{\cal G}$ can only be a symmetry of the former if the neutrino is a Majorana particle; the latter provides a dynamical modification of the leptonic weak couplings, reconstructing those of the Standard Model with a massless Majorana neutrino.
We study mixing and CP violation of three left-handed Majorana neutrinos in the limit of exactly degenerate masses, identify the weak-basis invariant relevant for CP violation and show that the leptonic mixing matrix is parametrized only by two angles and one phase. After the lifting of the degeneracy, this parametrization accommodates the present data on atmospheric and solar neutrinos, as well as double beta decay. Some of the leptonic mixing ansatze suggested in the literature correspond to special cases of this parametrization.
As is well-known, there exist totally three CP-violating phases in the leptonic sector if three ordinary neutrinos are massive Majorana particles. In this short note, we raise the question whether the number of sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos is three or four. An intuitive answer to this question would be three, which is also the total number of independent CP-violating phases. However, we give a counter example, in which three conditions are in general not sufficient for CP conservation. Only for all the lepton mas…
A possible extension of the Standard Model to include lepton number as local gauge symmetry is investigated. In such a model, anomalies are canceled by two extra fermions doublet. After leptonic gauge symmetry spontaneously broken, three active neutrinos may acquire non-zero Majorana masses through the modified Type-II seesaw mechanism. Constraints on the model from electro-weak precision measurements are studied. Due to the $Z_2$ discrete flavor symmetry, right-handed Majorana neutrinos can serve as cold dark matter candidate of the Universe. Constraint from dark matter relic abundance is cal…
We investigate purely leptonic decays of leptons $ł^{\prime-}\to l^-\barν_lν_{l^{\prime}}$ to distinguish Dirac or Majorana neutrinos. We derive the differences of the decay width (and associated quantities) between the two neutrino hypotheses by the effect of identical particles. Evidence from experimental data makes the hypothesis of Majorana neutrinos very unlikely and our results strongly favor the hypothesis of Dirac neutrinos (in the standard three-neutrino theory). Moreover, our exploration for decay widths can be extended to the polarization angles of leptons, which will inspire new in…
A dynamical origin of the Yukawa couplings is a promising scenario to explain the flavour puzzle. The focus of this letter is set on the role of the neutrino Majorana character: when an $O(2)_{N_R}$ flavour symmetry acts on the right-handed neutrino sector, the minimum of the scalar potential allows for large mixing angles -in contrast to the simplest quark case- and predicts a maximal Majorana phase. This leads to a strong correlation between neutrino mass hierarchy and mixing pattern. Realistic solutions point to the existence of three heavy right-handed neutrinos.
We analyze possible lepton-flavor-violating decays of the $Z^0$ particle in a minimal extension of the Standard Model, in which one right-handed neutral field for each family has been introduced. Such rare leptonic decays are induced by Majorana neutrinos at the first electroweak loop level and are generally not suppressed by the ordinary "see-saw" mechanism. In particular, we find that experimental bounds on branching ratios of the order of $10^{-5}-10^{-6}$ attainable at $LEP$ may impose constraints on lepton-flavor-mixing parameters and the masses of the heavy Majorana neutrinos.
The clockwork is an extra-dimensional set-up for generating light particles with exponentially suppressed or hierarchical couplings of light particles with N massive states having comparable masses near the threshold scale of the mechanism in theories which contain no small parameters at the fundamental level. We explore the prospect of charged lepton flavour violation (cLFV) in a clockwork framework which encompasses Dirac mass terms as well as Majorana mass terms for the new clockwork fermions. We deive the masses of the non zero clockwork Majorana masses, and new particles in a clockwork fr…
We consider a class of models of neutrino mixing with $S_4$ flavour symmetry and generalised CP symmetry, broken to $Z_2$ and $Z_2 \times {\rm CP}$ residual symmetries in the charged lepton and neutrino sectors, respectively. In this scheme, and up to discrete ambiguities, the neutrino mixing matrix is determined by two angles and one phase. We classify the phenomenologically viable mixing patterns, deriving predictions for the Dirac and Majorana CPV phases and for the effective Majorana mass in neutrinoless double beta decay.
We study the exactly degenerate case for three lefthanded Majorana neutrinos building a general parametrization for the leptonic mixing matrix characterized by two angles and one CP violating phase and identify a weak-basis invariant relevant, in this case, for CP violation. After lifting the degeneracy, this parametrization accommodates the present data on atmospheric and solar neutrinos, as well as neutrinoless double beta decay. Some of the leptonic mixing ansätze suggested in the literature correspond to special cases of this parametrization.
Leptonic CP violation is one of the most important topics in neutrino physics. CP violation in the neutrino sector is strongly related to the nature of neutrinos: whether they are Dirac or Majorana particles. In \cite{Popov:2021icg} we have shown that for Majorana neutrinos arance of nonzero Majorana CP-violating phases combined with strong magnetic field during supernova core-collaple can induce new resonances in neutrino oscillations, for example in $ν_e \to \barν_τ$ channel. In this contribution we further study new resonances in Majorana neutrino oscillations, in particular energy dependen…
We consider a class of models of neutrino mixing with $S_4$ lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual $Z_2$ and $Z_2 \times H^ν_{\rm CP}$ symmetries in the charged lepton and neutrino sectors, respectively, $H^ν_{\rm CP}$ being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters - two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Maj…
Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor mixing matrix to show their real shapes for the first time. The connections of the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current experimental data, we show how the six triangles formed by the effective Majorana neutrino masses \langle m\rangle_{αβ} (for α, β=…
In extensions of the Standard Model by Majorana fermions, the presence of additional CP violating phases has been shown to play a crucial role in lepton number violating processes. In this work we show that (Dirac and Majorana) CP violating phases can also lead to important effects in charged lepton flavour violating (cLFV) transitions and decays, in some cases with a significant impact for the predicted rates of cLFV observables. We conduct a thorough exploration of these effects in several cLFV observables, and discuss the implications for future observation. We emphasise how the presence of…
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 …
The extension of the standard model with new high-scale weakly coupled physics involving right-handed neutrinos in an effective field theory framework (SMNEFT) allows for a systematic study of heavy neutrinos phenomenology in current and future experiments. We exploit the outstanding angular resolution in future lepton colliders to study the sensitivity of forward-backward asymmetries to discover the possible single production of heavy Majorana neutrinos via $e^{+}e^{-} \to N ν$, followed by a purely leptonic decay $N \to μ^{-} μ^{+} ν$ or a semi-leptonic decay $N \to μ^{-} \mathrm{j} \mathrm{…
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
Neutralinos $\tildeχ^0$ in supersymmetric theories, the spin--1/2 Majorana--type superpartners of the U(1) and SU(2) neutral electroweak gauge bosons and SU(2) neutral Higgs bosons, are expected to be among light supersymmetric particles so that they can be produced copiouslyvia direct pair production and/or from cascade decays of other sparticles such as sleptons at the planned Large Hadron Collider and the prospective International Linear Collider. Considering the prospects of having both highly polarized neutralinos and possibility of reconstructing their decay rest frames, we provide a sys…
We investigate the sensitivity of some weak processes to the simplest extension of the Standard Model with Majorana neutrinos mixing in the leptonic sector. Values for mixing angles and masses compatible with several experimental accelerator data and the most recent neutrinoless double--$β$ decay limit were found.
Recently in [JHEP 09 (2021) 053], Wang et al. discussed the polynomial ring formed by flavor invariants in the leptonic sector with massive Majorana neutrinos. They have explicitly constructed the finite generating sets of the polynomial rings for both two-generation scenario and three-generation scenario. However, Wang et al.'s claim of the finiteness of the generating sets of the polynomial rings and their calculation by the approach of Hilbert series with generalized Molien-Weyl formula are both based on their assertion that the unitary group ${\rm U}(n,\mathbb{C})$ is reductive, which is u…
In this paper, we carry out a systematic study of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos. In particular, the emphasis is placed on the number of CP-violating phases in the presence of a partial mass degeneracy (e.g., $m^{}_1 = m^{}_2 \neq m^{}_3$) or a complete mass degeneracy $m^{}_1 = m^{}_2 = m^{}_3$, where $m^{}_i$ (for $i = 1, 2, 3$) stand for the masses of three ordinary neutrinos. In the canonical seesaw model with three right-handed neutrino singlets, CP-violating phases in the special case of a partial (e.g., …
If massive neutrinos are Majorana particles, then the lepton number should be violated in nature and neutrino-antineutrino oscillations $ν^{}_α\leftrightarrow \overlineν^{}_β$ (for $α, β= e, μ, τ$) will definitely take place. In the present paper, we study the properties of CP violation in neutrino-antineutrino oscillations with the non-unitary leptonic flavor mixing matrix, which is actually a natural prediction in the canonical seesaw model due to the mixing between light and heavy Majorana neutrinos. The oscillation probabilities $P(ν^{}_α\to \overlineν^{}_β)$ and $P(\overlineν^{}_α\to ν^{}…
We analyze the possibility of universality violation in diagonal leptonic decays of the $Z$ boson, in the context of interfamily "see-saw" models. In a minimal extension of the Standard Model with right-handed neutrino fields, we find that universality-breaking effects increase quadratically with the heavy Majorana neutrino mass and may be observed in the running $LEP$ experiments.
We respectfully reply to Wang et al.'s reply to our comment to their [JHEP $\textbf{09}$ (2021) 053]. Some more subtleties and details are discussed for hopefully better clarification and understanding, especially about the conditions in Hilbert's finiteness theorem. We also disprove Wang et al.'s incorrect assertion in their reply [arXiv:2110.13865 [hep-ph]] that there is an isomorphism between ${\rm U}(n,\mathbb{C})$ and ${\rm GL}(n,\mathbb{C})$. We give two proofs for our argument. One proof is in the context of Lie group for arbitrary positive integer $n$, and the other proof is in the con…
Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix M_ν. The most general case with all the free parameters of M_νbeing complex is discussed. We show that a favorable neutrino mixing pattern (with θ_12 \approx 35.3^\circ, θ_23=45^\circ, θ_13 \neq 0^\circ and δ=90^\circ) can naturally be derived from M_ν, if it has an approximate or softly-broken μ-τsymmetry. We also point out a different way to obtain the nearly tri-bimaximal neutrino mixing pattern with δ=0^\circ and non-vanishing Majorana p…
We study leptonic CP violation from a new perspective. For Majorana neutrinos, a new parametrization for leptonic mixing of the form $V=O_{23} O_{12} K_{a}^{i}\cdot O$ reveals interesting aspects that are less clear in the standard parametrization. We identify several important scenario-cases with mixing angles in agreement with experiment and leading to large leptonic CP violation. If neutrinos happen to be quasi-degenerate, this new parametrization might be very useful, e.g., in reducing the number of relevant parameters of models.
In models where the Standard Model is extended by Majorana fermions, interference effects due to the presence of CP violating phases have been shown to play a crucial role in lepton number violating processes. However, important effects can also arise in lepton number conserving, but charged lepton flavour violating (cLFV) transitions and decays. Here we show that the presence of CP violating (Dirac and Majorana) phases can have a striking impact for the predicted rates of cLFV observables. We explore the interference effects in several cLFV observables, carrying for the first time a thorough …
We construct extensions of the Standard Model with two Higgs doublets, where there are flavour changing neutral currents both in the quark and leptonic sectors, with their strength fixed by the fermion mixing matrices $V_{CKM}$ and $V_{PMNS}$. These models are an extension to the leptonic sector of the class of models previously considered by Branco, Grimus and Lavoura, for the quark sector. We consider both the cases of Dirac and Majorana neutrinos and identify the minimal discrete symmetry required in order to implement the models in a natural way.
We estimate the effect of leptonic CP violating phases in the minimal seesaw model with two heavy neutrinos $N$ by imposing the approximately $μ-τ$ symmetry on the model. For $N$ subject to the $μ-τ$ symmetry, we find that neutrinos show the normal mass hierarchy and obtain the general phase structure that contains only two phases which arise from $μ-τ$ symmetry breaking terms. To perform similar consideration for $N$ blind to the $μ-τ$ symmetry necessarily giving the inverted mass hierarchy, we assume the same phase structure. Our phases consist of six phases that need to take care of generic…
We consider a neutrino mass model where all leptonic mixing is induced by a heavy Majorana sector through the seesaw type I mechanism, while the Dirac mass matrices are diagonal. Such a pattern occurs naturally in grand unified theories. Constraints on the parameters of the models are considered and it is shown that a normal neutrino mass hierarchy is preferred. The lightest neutrino mass is typically small, leading to nonobservable rates for neutrinoless double beta decay in the normal hierarchy case.
In order to explain the recently reported result on the double beta decay $(0νββ)$ experiment, together with the earlier established data on LMA MSW solar and atmospheric neutrino oscillations, we generate the textures of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices within the framework of the see-saw mechanism in a model independent way. The leptonic mixings are generated from the texture of the right- handed Majorana mass matrices while keeping the Dirac neutrino mass matrices in diagonal forms.
We consider a minimal condition that predicts the 1-3 lepton mixing angle $θ_{13} \simeq θ_{\rm C}/\sqrt{2}$ with $θ_{\rm C}$ the Cabibbo angle, and give the improved prediction of $θ_{13}$. In the case of normal mass ordering, the theoretical value of $θ_{13}$ is predicted as $θ_{13}=8.6^\circ$, which is in good agreement with the current global best fit. In the case of inverted mass ordering, the theoretical value is predicted as $θ_{13}=9.7^\circ$, which is far from the current global best fit. We also study the leptonic CP violation. We show that any values of the leptonic Dirac CP phase $…
The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale, the quark and lepton mixing matrices are equal then for quasi-degenerate neutrinos, radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasi-degenerate neutrinos could, within this framework, be interpreted as a sign of quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in…
We further study the "complementary" Ansatz, Tr$(M_ν)$=0, for a prediagonal light Majorana type neutrino mass matrix. Previously, this was studied for the CP conserving case and the case where the two Majorana type CP violating phases were present but the Dirac type CP violating phase was neglected. Here we employ a simple geometric algorithm which enables us to "solve" the Ansatz including all three CP violating phases. Specifically, given the known neutrino oscillation data and an assumed two parameter (the third neutrino mass $m_3$ and the Dirac CP phase $δ$) family of inputs we predict the…
Assuming a minimal seesaw model with two heavy neutrinos (N), we examine effects of leptonic CP violation induced by approximate mu-tau symmetric interactions. As long as N is subject to the mu-tau symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from mu-tau symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases alpha and beta. The similar consideration is extended to N blind to the mu-tau symmetry. It is argued that N subject (blind)…
The leptonic sector in a recently proposed minimal extension of the standard model, in which the permutation symmetry S_3 is assumed to be an exact flavor symmetry at the weak scale, is revisited. We find that S_3 with an additional Z_{N} symmetry allows CP violating phases in the neutrino mixing. The leptonic sector contains six real parameters with two independent phases to describe charged lepton and neutrino masses and the neutrino mixing. The model predicts: an inverted spectrum of neutrino mass, tan theta_{23}=1+O(m_e^2/m_mu^2) and sin theta_{13}=m_e/sqrt{2}m_mu+O(m_em_mu/m_{tau}^2) sime…
We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
Motivated by recent measurements of a relatively large θ_{13} in the Daya Bay and RENO reactor neutrino experiments, we carry out a systematic analysis of the hybrid textures of Majorana neutrino mass matrix $M_ν$, which contain one texture zero and two equal nonzero matrix elements. We show that three neutrino masses (m_1, m_2, m_3) and three leptonic CP-violating phases (δ, ρ, σ) can fully be determined from two neutrino mass-squared differences (δm^2, Δm^2) and three flavor mixing angles (θ_{12}, θ_{23}, θ_{13}). Out of sixty logically possible patterns of $M_ν$, thirty-nine are found to be…
We show that there is a minimal discrete symmetry which leads to the extended flavour democracy scenario constraining the Dirac neutrino, the charged lepton and the Majorana neutrino mass term ($M_R$) to be all proportional to the democratic matrix, with all elements equal. In particular, this discreet symmetry forbids other large contributions to $M_R$, such as a term proportional to the unit matrix, which would normally be allowed by a $S_{3L}\times S_{3R}$ permutation symmetry. This feature is crucial in order to obtain large leptonic mixing, without violating 't Hooft's, naturalness princi…
We study the possibilities to detect Majorana neutrinos in $γγ$ colliders for different center of mass energies. We study the $W^\pm W^\pm l_j^{\mp} l_k^{\mp}$ ($l_j\equiv e ,μ,τ$) final states which are, due to leptonic number violation, a clear signature for intermediate Majorana neutrino contribution. Such a signal (final dileptons of the same sign) is not possible if the heavy neutrinos are Dirac particles. We present our results for the total cross-section as a function of the neutrino mass and the center of mass energies.
We explore generic features of the leptonic CP violation in the framework of the seesaw type I mechanism with similarity of the Dirac lepton and quarks mass matrices $m_D$. For this, we elaborate on the standard parametrization conditions which allow to simultaneously obtain the Dirac and Majorana phases. If the only origin of CP violation is the left-handed (LH) transformation which diagonalizes $m_D$ (similar to quarks), the leptonic CP violation is suppressed and the Dirac phase is close to $π$ or to $0$ with $\sin δ_{CP} \approx (\sin θ_{13}^q /\sin θ_{13}) \cos θ_{23} \sin δ_q \sim λ^2 \s…
We investigate the viability of thermal leptogenesis in type-I seesaw models with leptonic flavour symmetries that lead to tribimaximal neutrino mixing. We consider an effective theory with an A4 x Z3 x Z4 symmetry, which is spontaneously broken at a scale much higher than the electroweak scale. At the high scale, leptonic Yukawa interactions lead to exact tribimaximal mixing and the heavy Majorana neutrino mass spectrum is exactly degenerate. In this framework, leptogenesis becomes viable once this degeneracy is lifted either by renormalization group effects or by a soft breaking of the A4 sy…
If massive neutrinos are Majorana particles, then the lepton number should be violated and neutrino-antineutrino oscillations will take place. In this talk, we present the properties of CP violation in neutrino-antineutrino oscillations with a non-unitary leptonic flavor mixing matrix, which naturally arises in the type-I seesaw model due to the mixing between light and heavy Majorana neutrinos. Taking into account current experimental bounds on the leptonic unitarity violation, we show that the CP asymmetries induced by the non-unitary mixing parameters can significantly deviate from those in…
We consider the perturbatively modified tribimaximal (or bimaximal) mixing to estimate the (Dirac-type) CP phase in neutrino mixing matrix. The expressions for the CP phase are derived from the equivalence between the standard parametrization of the neutrino mixing matrix for the Majorana neutrino and modified tribimaximal or bimaximal mixing matrices with appropriate CP phases. Carrying out numerical analysis based on the current experimental results for neutrino mixing angles, we can predict the values of the CP phase for several possible cases.
The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the $μ$-$τ$ exchange symmetry are observed. Six types of texture non-zeros…
In the light of the recent measurement of the leptonic mixing angle $θ_{13}$, implications of the latest mixing data have been investigated for non-minimal textures of lepton mass matrices assuming the neutrinos to be Majorana like. Large number of possible texture specific lepton mass matrices have been examined for their compatibility with the lepton mixing data in the case of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses. Specifically, apart from other phenomenological quantities the implications of the lepton mixing angle $θ_{13}$ have been investigated on…
We have investigated a possible connection between the Majorana phases and geometric parameters of leptonic unitarity triangle(LUT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered two-texture zero neutrino mass model to obtain relation between Majorana phases and LUT parameters. In particular, we find that Majorana phases depend on only one of the thr…
