Tri-bimaximal Neutrino Mixing Research Articles

Neutrino mass model in the context of Δ(54)⊗Z2 ⊗ Z3 ⊗ Z4 flavor symmetries with Inverse Seesaw mechanism

Our analysis involves enhancing the Δ(54) flavor symmetry model with Inverse Seesaw mechanism along with two SM Higgs through the incorporation of distinct flavons. Additionally, we introduce supplementary Z2⊗Z3⊗Z4 symmetries to eliminate any undesirable components within our investigation. The exact tri-bimaximal neutrino mixing pattern undergoes a deviation as a result of the incorporation of extra flavons, leading to the emergence of a non-zero reactor angle θ13 that aligns with the latest experimental findings. It was found that for our model the atmospheric oscillation parameter occupies the lower octant for normal hierarchy case. We also examine the parameter space of the model for normal hierarchy to explore the Dirac CP (δCP), Jarlskog invariant parameter (J) and the Neutrinoless double-beta decay parameter (mββ) and found it in agreement with the neutrino latest data. Hence our model may be testable in the future neutrino experiments.

Nonzero θ13, CP-violation and neutrinoless double beta decay for neutrino mixing in the A4×Z2×Z3 flavor symmetry model

In this paper, we study the modification of the Altarelli–Feruglio [Formula: see text] flavor symmetry model by adding three singlet flavons [Formula: see text], [Formula: see text] and [Formula: see text] and the model is augmented with extra [Formula: see text] symmetry to prevent the unwanted terms in our study. The addition of these three flavons leads to two higher order corrections in the form of two perturbation parameters [Formula: see text] and [Formula: see text]. These corrections yield the deviation from exact tri-bimaximal (TBM) neutrino mixing pattern by producing a nonzero [Formula: see text] and other neutrino oscillation parameters which are consistent with the latest experimental data. In both the corrections, the neutrino masses are generated via Weinberg operator. The analysis of the perturbation parameters [Formula: see text] and [Formula: see text], shows that normal hierarchy (NH) and inverted hierarchy (IH) for [Formula: see text] do not change much. However, as the values of [Formula: see text] increase, [Formula: see text] occupies the lower octant for NH case. We further investigate the neutrinoless double beta decay parameter [Formula: see text] using the parameter space of the model for both normal and inverted hierarchies of neutrino masses.

Non-zero θ13 and δCP phase with A4 flavor symmetry and deviations to tri-bi-maximal mixing via Z2 × Z2 invariant perturbations in the neutrino sector

In this work, a flavour theory of a neutrino mass model based on A4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z2×Z2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δCP phase, the neutrino oscillation probability P(νμ→νe), the effective Majorana mass |mee| and |mνeeff|. A Z2×Z2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δCP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A4×Z2×Z2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalisation group effects or by a soft breaking of the A4 symmetry. In this context the implications for charged lepton flavour violation processes like μ→eγ, τ→eγ, τ→μγ are discussed.

Minimal modification of tri-bimaximal neutrino mixing and leptonic CP violation

We confront possible forms of the minimal modification of the tri-bimaximal (TBM) neutrino mixing matrix proposed by Kang and Kim (Phys. Rev. D 90, 077301 (2014)) with the latest global fit to neutrino data. One form among them is singled out by the current experimental results at 1σ confidence level (C.L.) The minimal modification of the TBM mixing matrix makes possible the prediction of Dirac-type CP phase in the Pontecorbo-Maki-Nakagawa-Sakata neutrino mixing matrix in terms of two neutrino mixing angles. By carrying out a numerical analysis based on the latest experimental results for neutrino mixing angles, we are able to present new results on the prediction of the Dirac-type CP phase. We also compare our results on CP violation with those from the current global fit at 1σ C.L.

Flavor origin of dark matter and its relation with leptonic nonzero \u03b813 and Dirac CP phase \u03b4

We propose a minimal extension of the standard model by including a U(1) flavor symmetry to establish a correlation between the relic abundance of dark matter, measured by WMAP and PLANCK satellite experiments and non-zero value of sin θ13 observed at DOUBLE CHOOZ, Daya Bay, RENO and T2K. The flavour symmetry is allowed to be broken at a high scale to a remnant {mathcal{Z}}_2 symmetry, which not only ensures the stability to the dark matter, but also gives rise to a modification to the existing A4-based tri-bimaximal neutrino mixing. This deviation in turn suggests the required non-zero value of sin θ13. We assume the dark matter to be neutral under the existing A4 symmetry while charged under the U(1) flavor symmetry. Hence in this set-up, the non-zero value of sin θ13 predicts the dark matter charge under U(1), which can be tested at various ongoing and future direct and collider dark matter search experiments. We also point out the involvement of nonzero leptonic CP phase δ, which plays an important role in the analysis.

Deviations in tribimaximal mixing from sterile neutrino sector

We explore the possibility of generating a non-zero Ue3 element of the neutrino mixing matrix from tribimaximal neutrino mixing by adding a light sterile neutrino to the active neutrinos. Small active–sterile mixing can provide the necessary deviation from tribimaximal mixing to generate a non-zero θ13 and atmospheric mixing θ23 different from maximal. Assuming no CP-violation, we study the phenomenological impact of sterile neutrinos in the context of current neutrino oscillation data. The tribimaximal pattern is broken in such a manner that the second column of tribimaximal mixing remains intact in the neutrino mixing matrix.

Unifying the flavor origin of dark matter with leptonic nonzeroθ13

We propose a flavor symmetric approach to unify the origin of dark matter (DM) with the non-zero $\theta_{13}$ in the lepton sector. In this framework, breaking of a $U(1)$ flavor symmetry to a remnant $Z_2$ ensures the stability of the DM and gives rise to a modification to the existing $A_4$-based tri-bimaximal neutrino mixing to attain the required non-zero $\sin \theta_{13}$. This results in a range of Higgs portal coupling of the DM which can be potentially accessible at various ongoing and future direct and collider search experiments.

Type II seesaw supersymmetric neutrino model forθ13≠0

Using the type II seesaw approach and properties of discrete flavor symmetry group representations, we build a supersymmetric $A_{4}\times A_{3}$\ neutrino model with $\theta_{13}\neq0$. After describing the basis of this model--which is beyond the minimal supersymmetric Standard Model--with a superfield spectrum containing flavons in $A_{4}\times A_{3}$\ representations, we first generate the tribimaximal neutrino mixing which is known to be in agreement with the mixing angles $\theta_{12}$ and $\theta_{23}$. Then, we give the scalar potential of the theory where the $A_{3}$ discrete subsymmetry is used to avoid the so-called sequestering problem. We \textrm{next} study the deviation from the tribimaximal mixing matrix which is produced by perturbing the neutrino mass matrix with a nontrivial $A_{4}$ singlet. Normal and inverted mass hierarchies are discussed numerically. We also study the breaking of $A_{4}$\ down to $Z_{3}$\ in the charged lepton sector, and use the branching ratio of the decay $\tau \rightarrow \mu \mu e$--which is allowed by the residual symmetry $Z_{3}$--to get estimations on the mass of one of the flavons and the cutoff scale $\Lambda$ of the model.

A 4 × U(1)PQ model for the lepton flavor structure and the strong CP problem

We present a model with $A_4 \times U(1)_{PQ}$ lepton flavor symmetry which explains the origin of the lepton flavor structure and also solves the strong $CP$ problem. Standard model gauge singlet fields, so-called "flavons", charged under the $A_4 \times U(1)_{PQ}$ symmetry are introduced and are coupled with the lepton and the Higgs sectors. The flavon vacuum expectation values (VEVs) trigger spontaneous breaking of the $A_4 \times U(1)_{PQ}$ symmetry. The breaking pattern of the $A_4$ accounts for the tri-bimaximal neutrino mixing and the deviation from it due to the non-zero $\theta_{13}$ angle, and the breaking of the $U(1)_{PQ}$ gives rise to a pseudo-Nambu-Goldstone boson, axion, whose VEV cancels the QCD $\theta$ term. We investigate the breaking of the $A_4 \times U(1)_{PQ}$ symmetry through an analysis on the scalar potential and further discuss the properties of the axion in the model, including its decay constant, mass and coupling with photons. It is shown that the axion decay constant is related with the right-handed neutrino mass through the flavon VEVs. Experimental constraints on the axion and their implications are also studied.

Discriminating Majorana neutrino phases in the light of lepton flavor violation and leptogenesis in type I+II seesaw models

We study the effects of Majorana neutrino phases in lepton flavor violation and the origin of matter–antimatter asymmetry through the mechanism of leptogenesis within the framework of a model where both type I and type II seesaw mechanisms can contribute to tiny neutrino masses. We parametrize the type I seesaw mass matrix by assuming it to give rise to a tri-bimaximal (TBM) type neutrino mixing which predicts [Formula: see text]. The type II seesaw mass matrix is then constructed in such a way that the necessary deviation from TBM mixing and the best fit values of neutrino parameters can be obtained when both type I and type II seesaw contributions are taken into account. Considering both subleading as well as equally dominating type II seesaw term, we first constrain the Majorana CP phases from the requirement of producing correct baryon asymmetry through leptogenesis and then incorporating the experimental bounds on lepton flavor violating decays [Formula: see text] and [Formula: see text].

Neutrino mixing with nonzero θ13 and CP violation in the 3-3-1 model based on A4 flavor symmetry

We propose a 3-3-1 model with neutral fermions based on [Formula: see text] flavor symmetry responsible for fermion masses and mixings with nonzero [Formula: see text]. To get realistic neutrino mixing, we just add a new [Formula: see text] triplet being in [Formula: see text] under [Formula: see text]. The neutrinos get small masses from two [Formula: see text] antisextets and one [Formula: see text] triplet. The model can fit the present data on neutrino masses and mixing as well as the effective mass governing neutrinoless double beta decay. Our results show that the neutrino masses are naturally small and a little deviation from the tri-bimaximal neutrino mixing form can be realized. The Dirac CP violation phase [Formula: see text] is predicted to either [Formula: see text] or [Formula: see text] with [Formula: see text].

Nonzeroθ13and leptogenesis in a type-I seesaw model withA4symmetry

In the light of recent discovery of nonzero $\theta_{13}$, we have analyzed the Altarelli-Feruglio $A_4$ flavor symmetry model extended with additional flavon. The inclusion of the new field leads to the deviation from exact tri-bimaximal neutrino mixing pattern in the context of type-I see-saw by producing a nonzero $\theta_{13}$ consistent with the recent experimental results at the leading order. A sum rule for light neutrino masses is also obtained in this context. The set-up constraints the two Majorana phases involved in the lepton mixing matrix in terms of $A_4$ parameter space. We have shown that a nonzero lepton asymmetry can be generated while next-to-leading order contributions to the neutrino Yukawa couplings are considered. The two Majorana phases play crucial role in CP-asymmetry parameter and the involvement of $\theta_{13}$ in it, is exercised.

Predicting CP violation in deviation from tri-bimaximal mixing of neutrinos

We study the CP violation in the deviation from the tri-bimaximal (TBM) mixing of neutrinos. We examine nontrivial relations among the mixing angles and the CP violating Dirac phase in the typical four cases of the deviation from the TBM. The first two cases are derived by the additional rotation of the 2-3 or 1-3 generations of neutrinos in the TBM basis. The other two cases are given by the additional rotation of the 1-3 or 1-2 generations of charged leptons with the TBM neutrinos. These four cases predict different relations among three mixing angles and the CP violating Dirac phase. The rotation of the 2-3 generations of neutrinos in the TBM basis predicts sin2θ12< 1/3, and the CP violating Dirac phase to be ±(0.09π–0.76π) for NH (±(0.15π–0.73π) for IH) depending on sin2θ23. The rotation of the 1-3 generations of neutrinos in the TBM basis gives sin2θ12> 1/3. The CP violating Dirac phase is not constrained by the input of the present experimental data. For the case of the 1-3 and 1-2 rotations of charged leptons in the TBM basis, the CP violating Dirac phase is predicted in ±(0.35π–0.60π) depending on sin2θ12for both normal hierarchy (NH) and inverted hierarchy (IH) cases. We also discuss the specific case that θ13is related with the Cabibbo angle λ such as [Formula: see text], in which the maximal CP violation is preferred. The CP violating Dirac phase can distinguish the lepton flavor mixing patterns at T2K and NOνA experiments in the future.

Minimal modifications to the Tri-Bimaximal neutrino mixing

Abstract In light of the observation of a relatively large θ 13, the ever popular Tri-Bimaximal (TBM) neutrino mixing which predicts a vanishing θ 13 needs modifications. In this paper, we shall discuss the possibility of modifying it in a minimal way to fulfil this task. In the first part, a neutrino mass matrix with three independent parameters, which leads to the TM2 mixing, is obtained by analogy with that for the TBM mixing. In the second part, a model that can realize the TM2 mixing is constructed with flavor symmetries A 4 × U(1) × Z 2 × Z 2 × Z 2. It is the variant of a model that gives the TBM mixing, with only one more flavon field included. Furthermore, the imaginary vacuum expectation value (VEV) of this flavon breaks the imposed CP symmetry and results in θ 23 = 45° and the maximal CP violation. Besides, this model building approach can be generalized to the TM1 mixing in a straightforward way.

The dark side of θ 13, δ CP , leptogenesis and inflation in type-I seesaw

In the context of the type-I seesaw mechanism, it is known that $\theta_{13}$ is zero and leptogenesis can not be realized if there exists a residual flavor symmetry resulting in the Tri-Bimaximal neutrino mixing pattern. We propose a simple framework where additional particles, odd under a $Z_2$ symmetry, break the residual flavor symmetry and the lightest of the $Z_2$ odd particles is the dark matter candidate. As as result, nonzero $\theta_{13}$, $\delta_{CP}$, leptogenesis and the correct dark matter density can be accommodated. On the other hand, a $Z_2$ odd scalar can play the role of the inflaton with mass of $10^{13}$ GeV motivated by the recent BICEP2 results. Interestingly, the model can "generate" $\delta_{CP} \simeq -\pi/2$, preferred by the T2K experiment in the normal hierarchy neutrino mass spectrum.

Deviations from tribimaximal neutrino mixing using a model with Δ(27) symmetry

We present a model of neutrino mixing based on the flavor group Δ(27) in order to account for the observation of a nonzero reactor mixing angle (θ13). The model provides a common flavor structure for the charged-lepton and the neutrino sectors, giving their mass matrices a "circulant-plus-diagonal" form. Mass matrices of this form readily lead to mixing patterns with realistic deviations from tribimaximal mixing, including nonzero θ13. With the parameters constrained by existing measurements, our model predicts an inverted neutrino mass hierarchy. We obtain two distinct sets of solutions in which the atmospheric mixing angle lies in the first and the second octants. The first (second) octant solution predicts the lightest neutrino mass, m3~29 meV (m3~65 meV ) and the CP phase, [Formula: see text], offering the possibility of large observable CP violating effects in future experiments.

Neutrino mass and mixing in the 3-3-1 model and S 3 flavor symmetry with minimal Higgs content

A new S3 flavor model based on the SU(3)C ⊗ SU(3)L ⊗ U(1)X gauge symmetry responsible for fermion masses and mixings different from our previous work [14, 17] is constructed. The new feature is a two-dimensional representation of a Higgs anti-sextet under S3, which is responsible for neutrino masses and mixings. The neutrinos acquire small masses from only an anti-sextet of SU(3), which is in a doublet under S3. If the difference of components of the anti-sextet is regarded as a small perturbation, S3 is equivalently broken into identity, the corresponding neutrino mass mixing matrix acquires the most general form, and the model can fit the latest data on neutrino oscillations. This way of symmetry breaking helps us reduce a content in the Higgs sector, to only one anti-sextet instead of two as in our previous work [14]. Our results show that the neutrino masses are naturally small and a small deviation from the tri-bimaximal neutrino mixing form can be realized. The Higgs potential of the model as well as the minimization conditions and gauge boson masses and mixings are also considered.

A NewS4Flavor Symmetry in 3-3-1 Model with Neutral Fermions

A newS4flavor model based onSU(3)C⊗SU(3)L⊗U(1)Xgauge symmetry responsible for fermion masses and mixings is constructed. The neutrinos get small masses from only an antisextet ofSU(3)Lwhich is in a doublet underS4. In this work, we assume the VEVs of the antisextet differ from each other underS4and the difference of these VEVs is regarded as a small perturbation, and then the model can fit the experimental data on neutrino masses and mixings. Our results show that the neutrino masses are naturally small and a deviation from the tribimaximal neutrino mixing form can be realized. The quark masses and mixing matrix are also discussed. The number of required Higgs multiplets is less and the scalar potential of the model is simpler than those of the model based onS3and our previousS4model. The assignation of VEVs to antisextet leads to the mixing of the new gauge bosons and those in the standard model. The mixing in the charged gauge bosons as well as the neutral gauge bosons is considered.

THE D4FLAVOR SYMMETRY IN 3-3-1 MODEL WITH NEUTRAL LEPTONS

We construct a D4flavor model based on SU(3)C⊗SU(3)L⊗U(1)Xgauge symmetry responsible for fermion masses and mixings. The neutrinos get small masses from antisextets which are in a singlet and a doublet under D4. If the D4symmetry is violated as perturbation by a Higgs triplet under SU(3)Land lying in [Formula: see text] of D4, the corresponding neutrino mass mixing matrix gets the most general form. In this case, the model can fit the experimental data in 2012 on neutrino masses and mixing. Our results show that the neutrino masses are naturally small and a little deviation from the tribimaximal neutrino mixing form can be realized. The quark masses and mixing matrix are also discussed. In the model under consideration, the CKM matrix can be different from the unit matrix. The scalar potential of the model is more simpler than those of the model based on S3and S4. Assignation of VEVs to antisextets leads to the mixing of the new gauge bosons and those in the Standard Model. The mixing in the charged gauge bosons as well as the neutral gauge boson is considered.

Deviations from tri-bimaximal neutrino mixing using type II seesaw

We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the μ–τ symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like A4 whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero θ13. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure (m1,−m2,m3) and (m1,m2,m3), we numerically fit the type I seesaw term by taking oscillation as well as cosmology data and then compute the predictions for neutrino parameters after the type II seesaw term is introduced. We consider a minimal structure of the type II seesaw term and check whether the predictions for neutrino parameters lie in the 3σ range. We also outline two possible flavor symmetry models to justify the minimal structure of the type II seesaw term considered in the analysis.