A4-based tri-bimaximal mixing within inverse and linear seesaw schemes

We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A₄$A_4$ flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the inverse seesaw does not. The models also lead to potentially sizeable decay rates for lepton flavor violating processes, tightly related by the assumed flavor symmetry.     

General neutrino mass spectrum and mixing properties in seesaw mechanisms

Neutrinos stand out among the elementary particles because of their unusually small masses.Various seesaw mechanisms attempt to explain this fact.In this work,applying insights from matrix theory,we are in a position to treat variants of seesaw mechanisms in a general manner.Specifically,using Weyl's inequalities,we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos.We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos,shifted at most by the maximal strength of the coupling to the light neutrino sector.We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy.For higher-dimensional cases the inverse eigenvalue methods are used.In particular,for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones,i.e.if the respective mass submatrix is positive definite,then large masses are provided by matrices with large elements accumulated on the diagonal.Finally,the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis.This general observation concerning neutrino mixing,together with results on the mass spectrum properties,opens directions for further neutrino physics studies using matrix analysis.     

Realizing tri-bimaximal mixing in minimal seesaw model with S4 family symmetry

In this Letter, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group S4 as the family symmetry. In order to constrain the form of superpotential, a Z3 symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of O(0.01) at NLO. The mechanism to get the particular scalar VEV alignments used is also presented. Phenomenologically, the mass spectrum is of normal hierarchy with m₁=0, and ∑mi and |mee| are about 0.058 eV and 0.003 eV respectively.     

New type of seesaw mechanism for neutrino masses

In a wide class of unified models there is an additional (and possibly dominant) term in the neutrino mass formula that under the simplest assumption takes the form M(nu)=(M(N)+M(T)(N))u/M(G), where M(N) is the neutrino Dirac mass matrix, and u=O(M(W)). This makes possible highly predictive models. A generalization of this form yields realistic neutrino masses and mixings more readily than the usual seesaw formula in some models. The conditions for resonant enhancement of leptogenesis can occur naturally in such models.     

Deviation from tri-bimaximal mixing and large reactor mixing angle

Recent observations for a non-zero _θ13${\theta }_{13}$ have come from various experiments. We study a model of lepton mixing with a 2–3 flavor symmetry to accommodate the sizable _θ13${\theta }_{13}$ measurement. In this work, we derive deviations from the tri-bimaximal (TBM) pattern arising from breaking the flavor symmetry in the neutrino sector, while the charged leptons contribution has been discussed in a previous work. Contributions from both sectors towards accommodating the non-zero _θ13${\theta }_{13}$ measurement are presented.     

Non-unitary neutrino mixing and CP violation in the minimal inverse seesaw model

We propose a simplified version of the inverse seesaw model, in which only two pairs of the gauge-singlet neutrinos are introduced, to interpret the observed neutrino mass hierarchy and lepton flavor mixing at or below the TeV scale. This “minimal” inverse seesaw scenario (MISS) is technically natural and experimentally testable. In particular, we show that the effective parameters describing the non-unitary neutrino mixing matrix are strongly correlated in the MISS, and thus, their upper bounds can be constrained by current experimental data in a more restrictive way. The Jarlskog invariants of non-unitary CP violation are calculated, and the discovery potential of such new CP-violating effects in the near detector of a neutrino factory is discussed.     

Comparing trimaximal mixing and its variants with deviations from tri-bimaximal mixing

We analyze in detail the predictions of “trimaximal” neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually can have the same forms as for tri-bimaximal mixing. The phenomenology of these alternative scenarios and their mixing angle and CP phase correlations are studied. We emphasize how trimaximal mixing scenarios can be distinguished experimentally from broken tri-bimaximal mixing.     

Possible alternatives to tri-bimaximal mixing

Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U _e3|, sin ² θ ₁₂ and sin ² θ ₂₃ are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry.     

Minimal supergravity scalar neutrino dark matter and inverse seesaw neutrino masses

We show that within the inverse seesaw mechanism for generating neutrino masses, minimal supergravity naturally provides the scalar neutrino as the lightest superparticle. We also demonstrate that such schemes naturally reconcile the small neutrino masses with the correct relic scalar neutrino dark matter abundance and accessible direct detection rates in nuclear recoil experiments. This way, inverse seesaw minimal supergravity offers a common solution to the generation of the neutrino mass and to the origin of dark matter.     

Determining horizontal symmetry from neutrino mixing

We argue that the best way to determine horizontal symmetry is from neutrino mixing and proceed to show that the only finite group capable of yielding the tribimaximal mixing for all Yukawa couplings is S4, or any group containing it. The method used is largely group theoretical, but it can be implemented by dynamical schemes in which the Higgs expectation values introduced to break S4 spontaneously are uniquely determined up to an unknown scale for each.     

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α≈90°$\alpha \approx 90\text{°}$. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5)$\mathit{SU}(5)$, a discrete family symmetry such as A₄$A_4$ or S₄$S_4$, a shaping symmetry including products of Z₂${\mathbb{Z}}_2$ and Z₄${\mathbb{Z}}_4$ groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α≈90°$\alpha \approx 90\text{°}$ by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.     

Bimaximal mixing in seesaw models

Neutrino masses and mixing are discussed in seesaw models assuming hierarchical structure of Dirac masses and predicting bimaximal mixing for three light neutrinos.     

Low-scale neutrino seesaw mechanism and scalar dark matter

Recently the AMS-02 experiment has released the data of positron fraction with a very small statistical error. Because of the small error, it is no longer easy to fit the data with single dark matter for a fixed diffusion model and dark matter profile. In this paper, we propose a new interpretation of the data: that it originates from decay of two-component dark matter. This interpretation gives a rough threshold of the lighter DM component. When DM decays into leptons, the positron fraction in the cosmic rays depends on the flavor of the final states, and this is fixed by imposing a non-Abelian discrete symmetry on our model. By assuming two gauge-singlet fermionic decaying DM particles, we show that a model with non-Abelian discrete flavor symmetry, e.g. $T_{13}$ , can give a much better fitting to the AMS-02 data compared with a single-component dark matter scenario. Few dimension-six operators of the universal leptonic decay of DM particles are allowed in our model, since its decay operators are constrained by the $T_{13}$ symmetry. We also show that the lepton masses and mixings are consistent with current experimental data, due to the flavor symmetry.     

Maximal atmospheric neutrino mixing from texture zeros and quasi-degenerate neutrino masses

It is well known that, in the basis where the charged-lepton mass matrix is diagonal, there are seven cases of two texture zeros in Majorana neutrino mass matrices that are compatible with all experimental data. We show that two of these cases, namely B₃ and B₄ in the classification of Frampton, Glashow and Marfatia, are special in the sense that they automatically lead to near-maximal atmospheric neutrino mixing in the limit of a quasi-degenerate neutrino mass spectrum. This property holds true irrespective of the values of the solar and reactor mixing angles because, for these two cases, in the limit of a quasi-degenerate spectrum, the second and third row of the lepton mixing matrix are, up to signs, approximately complex-conjugate to each other. Moreover, in the same limit the aforementioned cases also develop a maximal CP-violating CKM-type phase, provided the reactor mixing angle is not too small.